1. Measuring Angles

In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 135°

In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 87.177°

In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 𝜋

In Exercises 1–6, the measure of an angle is given. Classify the angle as acute, right, obtuse, or straight. 𝜋/2

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

7𝜋 6

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

3𝜋 4

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

7𝜋 4

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

_ 2𝜋 3

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

_ 5𝜋 6

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

_ 5𝜋 4

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

_ 7𝜋 4

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

16𝜋 3

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

14𝜋 3

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

120°

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

-210°

In Exercises 41–56, use the circle shown in the rectangular coordinate system to draw each angle in standard position. State the quadrant in which the angle lies. When an angle's measure is given in radians, work the exercise without converting to degrees.

420°

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. 395°

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. -150°

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. -760°

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. 17𝜋 5

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. 25𝜋 6

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. -𝜋 40

Use the circle shown in the rectangular coordinate system to solve Exercises 81–86. Find two angles, in radians, between -2𝜋 and 2𝜋 such that each angle's terminal side passes through the origin and the given point.

A

Use the circle shown in the rectangular coordinate system to solve Exercises 81–86. Find two angles, in radians, between -2𝜋 and 2𝜋 such that each angle's terminal side passes through the origin and the given point.

D

Use the circle shown in the rectangular coordinate system to solve Exercises 81–86. Find two angles, in radians, between -2𝜋 and 2𝜋 such that each angle's terminal side passes through the origin and the given point.

F

Use the circle shown in the rectangular coordinate system to solve Exercises 81–86. Find two angles, in radians, between -2𝜋 and 2𝜋 such that each angle's terminal side passes through the origin and the given point.

E

In Exercises 87–90, find the absolute value of the radian measure of the angle that the second hand of a clock moves through in the given time. 55 seconds

In Exercises 87–90, find the absolute value of the radian measure of the angle that the second hand of a clock moves through in the given time. 3 minutes and 40 seconds

In Exercises 8–12, draw each angle in standard position. 5𝜋 6

In Exercises 8–12, draw each angle in standard position. 8𝜋 3

In Exercises 8–12, draw each angle in standard position. -135°

In Exercises 13–17, find a positive angle less than 360° or 2𝜋 that is coterminal with the given angle. -445°

In Exercises 13–17, find a positive angle less than 360° or 2𝜋 that is coterminal with the given angle. 31𝜋 6

In Exercises 39–40, let θ be an angle in standard position. Name the quadrant in which θ lies. tan θ > 0 and sec θ > 0

In Exercises 39–40, let θ be an angle in standard position. Name the quadrant in which θ lies. tan θ > 0 and cos θ < 0

Find a positive angle less than 2𝜋 that is coterminal with 16𝜋 3

In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places. sin 38°

In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places. tan 32.7°

In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places. csc 17°

In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places. cos 𝜋 10

In Exercises 39–48, use a calculator to find the value of the trigonometric function to four decimal places. cot 𝜋 12

In Exercises 55–58, use a calculator to find the value of the acute angle θ to the nearest degree. sin θ = 0.2974

In Exercises 55–58, use a calculator to find the value of the acute angle θ to the nearest degree. tan θ = 4.6252

In Exercises 59–62, use a calculator to find the value of the acute angle θ in radians, rounded to three decimal places. cos θ = 0.4112

In Exercises 59–62, use a calculator to find the value of the acute angle θ in radians, rounded to three decimal places. tan θ = 0.4169

In Exercises 99–104, find two values of θ, 0 ≤ θ < 2𝜋, that satisfy each equation. _ sin θ = √2 2

In Exercises 99–104, find two values of θ, 0 ≤ θ < 2𝜋, that satisfy each equation. _ sin θ = - √2 2

CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. One degree, written 1°, represents ____________ of a complete rotation.

CONCEPT PREVIEW Fill in the blank to correctly complete each sentence. One minute, written 1' , is ________________ of a degree.

Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 30°

Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 45°

Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 54°

Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 10°

Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 89°

Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 14° 20'

Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 50° 40' 50"

Find the measure of each marked angle. See Example 2.

Find the measure of each marked angle. See Example 2.

Find the measure of each marked angle. See Example 2.

Find the measure of each marked angle. See Example 2.

Find the measure of each marked angle. See Example 2.

Find the measure of each marked angle. See Example 2.

Find the measure of each marked angle. See Example 2 supplementary angles with measures 10𝓍 + 7 and 7𝓍 + 3 degrees

Find the measure of each marked angle. See Example 2 supplementary angles with measures 6𝓍 ― 4 and 8𝓍― 12 degrees

Find the measure of each marked angle. See Example 2 complementary angles with measures 9𝓍 + 6 and 3𝓍 degrees

Find the measure of each marked angle. See Example 2 complementary angles with measures 3𝓍 ― 5 and 6𝓍 ― 40 degrees

Find the measure of the smaller angle formed by the hands of a clock at the following times.

Find the measure of the smaller angle formed by the hands of a clock at the following times. 3:15

Find the measure of the smaller angle formed by the hands of a clock at the following times. 8:20

Perform each calculation. See Example 3. 75° 15' + 83° 32'

Perform each calculation. See Example 3. 47° 29' ― 71° 18'

Perform each calculation. See Example 3. 90° ― 51° 28'

Perform each calculation. See Example 3. 90° ― 17° 13'

Perform each calculation. See Example 3. 90° ― 36° 18' 47"

Perform each calculation. See Example 3. 55° 30' + 12° 44' ― 8° 15'

Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. See Example 4(a). 82° 30'

Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. See Example 4(a). 112° 15'

Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. See Example 4(a). ― 70° 48'

Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. See Example 4(a). 38° 42' 18"

Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. See Example 4(a). 274° 18' 59"

Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. See Example 4(b). 174.255°

Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. See Example 4(b). ―25.485°

Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. See Example 4(b). 59.0854°

Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. See Example 4(b). 102.3771°

Convert each angle measure to degrees, minutes, and seconds. If applicable, round to the nearest second. See Example 4(b). 122.6853°

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. 26° 30'

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. ―203° 20'

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. 541°

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. ―541°

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. 1000°

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. 8440°

Find the angle of least positive measure (not equal to the given measure) that is coterminal with each angle. See Example 5. ―5280°

Give two positive and two negative angles that are coterminal with the given quadrantal angle. 90°

Give two positive and two negative angles that are coterminal with the given quadrantal angle. 0°

Give two positive and two negative angles that are coterminal with the given quadrantal angle. 270°

Write an expression that generates all angles coterminal with each angle. Let n represent any integer. 135°

Write an expression that generates all angles coterminal with each angle. Let n represent any integer. ―90°

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. 174 °

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. 300 °

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. ―61 °

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. 90 °

Concept Check Sketch each angle in standard position. Draw an arrow representing the correct amount of rotation. Find the measure of two other angles, one positive and one negative, that are coterminal with the given angle. Give the quadrant of each angle, if applicable. ―90 °

Solve each problem. See Example 6. Revolutions of a Turntable A turntable in a shop makes 45 revolutions per min. How many revolutions does it make per second?

Solve each problem. See Example 6. Rotating Pulley A pulley rotates through 75° in 1 min. How many rotations does the pulley make in 1 hr?

Solve each problem. See Example 6. Surveying One student in a surveying class measures an angle as 74.25°, while another student measures the same angle as 74° 20' . Find the difference between these measurements, both to the nearest minute and to the nearest hundredth of a degree.

Give the measures of the complement and the supplement of an angle measuring 35° .

Find the angle of least positive measure that is coterminal with each angle. 792°

Solve each problem. Rotating Propeller The propeller of a speedboat rotates 650 times per min. Through how many degrees does a point on the edge of the propeller rotate in 2.4 sec?​​

Solve each problem. Rotating Pulley A pulley is rotating 320 times per min. Through how many degrees does a point on the edge of the pulley move in 2/3 sec?

Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to decimal degrees. If applicable, round to the nearest second or the nearest thousandth of a degree. 119° 08' 03"

Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to decimal degrees. If applicable, round to the nearest second or the nearest thousandth of a degree. 275.1005°

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II. I II. 1. sin 83° A. 88.09084757° 2. B. 63.25631605° 3. C. 1.909152433° 4. D. 17.45760312° 5. E. 0.2867453858 6. F. 1.962610506 7. G. 14.47751219° 8. H. 1.015426612 9. I. 1.051462224 10. J. 0.9925461516

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II. I II. 1. A. 88.09084757° 2. cos⁻¹ 0.45 B. 63.25631605° 3. C. 1.909152433° 4. D. 17.45760312° 5. E. 0.2867453858 6. F. 1.962610506 7. G. 14.47751219° 8. H. 1.015426612 9. I. 1.051462224 10. J. 0.9925461516

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II. I II. 1. A. 88.09084757° 2. B. 63.25631605° 3. tan 16° C. 1.909152433° 4. D. 17.45760312° 5. E. 0.2867453858 6. F. 1.962610506 7. G. 14.47751219° 8. H. 1.015426612 9. I. 1.051462224 10. J. 0.9925461516

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II. I II. 1. A. 88.09084757° 2. B. 63.25631605° 3. C. 1.909152433° 4. cot 27° D. 17.45760312° 5. E. 0.2867453858 6. F. 1.962610506 7. G. 14.47751219° 8. H. 1.015426612 9. I. 1.051462224 10. J. 0.9925461516

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II. I II. 1. A. 88.09084757° 2. B. 63.25631605° 3. C. 1.909152433° 4. D. 17.45760312° 5. sin⁻¹ 0.30 E. 0.2867453858 6. F. 1.962610506 7. G. 14.47751219° 8. H. 1.015426612 9. I. 1.051462224 10. J. 0.9925461516

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II. I II. 1. A. 88.09084757° 2. B. 63.25631605° 3. C. 1.909152433° 4. D. 17.45760312° 5. E. 0.2867453858 6. sec 18° F. 1.962610506 7. G. 14.47751219° 8. H. 1.015426612 9. I. 1.051462224 10. J. 0.9925461516

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II. I II. 1. A. 88.09084757° 2. B. 63.25631605° 3. C. 1.909152433° 4. D. 17.45760312° 5. E. 0.2867453858 6. F. 1.962610506 7. scs 80° G. 14.47751219° 8. H. 1.015426612 9. I. 1.051462224 10. J. 0.9925461516

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II. I II. 1. A. 88.09084757° 2. B. 63.25631605° 3. C. 1.909152433° 4. D. 17.45760312° 5. E. 0.2867453858 6. F. 1.962610506 7. G. 14.47751219° 8. tan⁻¹ 30 H. 1.015426612 9. I. 1.051462224 10. J. 0.9925461516

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II. I II. 1. A. 88.09084757° 2. B. 63.25631605° 3. C. 1.909152433° 4. D. 17.45760312° 5. E. 0.2867453858 6. F. 1.962610506 7. G. 14.47751219° 8. H. 1.015426612 9. csc⁻¹ 4 I. 1.051462224 10. J. 0.9925461516

CONCEPT PREVIEW Match each trigonometric function value or angle in Column I with its appropriate approximation in Column II. I II. 1. A. 88.09084757° 2. B. 63.25631605° 3. C. 1.909152433° 4. D. 17.45760312° 5. E. 0.2867453858 6. F. 1.962610506 7. G. 14.47751219° 8. H. 1.015426612 9. I. 1.051462224 10. cot⁻¹ 30 J. 0.9925461516

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1. sin 38° 42'

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1. cos 41° 24'

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1. csc 145° 45'

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1. cot 183° 48'

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1. tan 421° 30'

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1. tan(-80° 06')

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1. 1 ————— sec 14.8°

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1. cot(90°-4.72°)

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1. cos(90°-3.69°)

Use a calculator to approximate the value of each expression. Give answers to six decimal places. In Exercises 21–28, simplify the expression before using the calculator. See Example 1. 1 —————— csc(90°-51°)

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2. tan θ = 6.4358841

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2. sin θ = 0.84802194

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2. csc θ = 1.3861147

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2. sec θ = 1.1606249

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2. cos θ = 0.85536428

Find a value of θ in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. See Example 2. cot θ = 0.21563481

Use a calculator to evaluate each expression. sin 35° cos 55° + cos 35° sin 55°

Use a calculator to evaluate each expression. 2 sin 25°13' cos 25°13' - sin 50°26'

Use a calculator to evaluate each expression. cos 75°29' cos 14°31' - sin 75°29' sin 14°31'

Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. sin 10° + sin 10° = sin 20°

Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. cos 40° = 2 cos 20°

Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. cos 70° = 2 cos² 35° - 1

Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. 2 cos 38°22' = cos 76°44'

Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. ½ sin 40° = sin [½ (40°)]

Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. tan² 72°25' + 1 = sec² 72°25'

Use a calculator to determine whether each statement is true or false. A true statement may lead to results that differ in the last decimal place due to rounding error. cos(30° + 20°) = cos 30° + cos 20°

Find two angles in the interval [0°, 360°) that satisfy each of the following. Round answers to the nearest degree. sin θ = 0.52991926

Find two angles in the interval [0°, 360°) that satisfy each of the following. Round answers to the nearest degree. cos θ = 0.10452846

Find two angles in the interval [0°, 360°) that satisfy each of the following. Round answers to the nearest degree. tan θ = 0.70020753

(Modeling) Grade Resistance Solve each problem. See Example 3. Find the grade resistance, to the nearest ten pounds, for a 2400-lb car traveling on a -2.4° downhill grade.

(Modeling) Grade Resistance Solve each problem. See Example 3. A 3000-lb car traveling uphill has a grade resistance of 150 lb. Find the angle of the grade to the nearest tenth of a degree.

(Modeling) Grade Resistance Solve each problem. See Example 3. A car traveling on a -3° downhill grade has a grade resistance of -145 lb. Determine the weight of the car to the nearest hundred pounds.

(Modeling) Speed of Light When a light ray travels from one medium, such as air, to another medium, such as water or glass, the speed of the light changes, and the light ray is bent, or refracted, at the boundary between the two media. (This is why objects under water appear to be in a different position from where they really are.) It can be shown in physics that these changes are related by Snell's law c₁ = sin θ₁ , c₂ sin θ₂ where c₁ is the speed of light in the first medium, c₂ is the speed of light in the second medium, and θ₁ and θ₂ are the angles shown in the figure. In Exercises 81 and 82, assume that c₁ = 3 x 10⁸ m per sec. Find the speed of light in the second medium for each of the following. a. θ₁ = 46°, θ₂ = 31° b. θ₁ = 39°, θ₂ = 28°

(Modeling) Fish's View of the World The figure shows a fish's view of the world above the surface of the water. (Data from Walker, J., 'The Amateur Scientist,' Scientific American.) Suppose that a light ray comes from the horizon, enters the water, and strikes the fish's eye. Assume that this ray gives a value of 90° for angle θ₁ in the formula for Snell's law. (In a practical situation, this angle woul​​d probably be a little less than 90°.) The speed of light in water is about 2.254 x 10⁸ m per sec. Find angle θ₂ to the nearest tenth.

(Modeling) Length of a Sag Curve When a highway goes downhill and then uphill, it has a sag curve. Sag curves are designed so that at night, headlights shine sufficiently far down the road to allow a safe stopping distance. See the figure. S and L are in feet. The minimum length L of a sag curve is determined by the height h of the car's headlights above the pavement, the downhill grade θ₁ < 0°, the uphill grade θ₂ > 0°, and the safe stopping distance S for a given speed limit. In addition, L is dependent on the vertical alignment of the headlights. Headlights are usually pointed upward at a slight angle α above the horizontal of the car. Using these quantities, for a 55 mph speed limit, L can be modeled by the formula (θ₂ - θ₁)S² L = ————————— , 200(h + S tan α) where S < L. (Data from Mannering, F., and W. Kilareski, Principles of Highway Engineering and Traffic Analysis, Second Edition, John Wiley and Sons.) Compute length L, to the nearest foot, if h = 1.9 ft, α = 0.9°, θ₁ = -3°, θ₂ = 4°, and S = 336 ft.

Use a calculator to approximate the value of each expression. Give answers to six decimal places. sec 222° 30'

Use a calculator to approximate the value of each expression. Give answers to six decimal places. tan 11.7689°

Use a calculator to approximate the value of each expression. Give answers to six decimal places. sec 58.9041°

Find a value of θ, in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. cot θ = 1.1249386

Find a value of θ, in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. sec θ = 1.2637891

Find a value of θ, in the interval [0°, 90°) that satisfies each statement. Give answers in decimal degrees to six decimal places. csc θ = 9.5670466

Find two angles in the interval [0°, 360°) that satisfy each of the following. Round answers to the nearest degree. tan θ = 1.3763819

Determine whether each statement is true or false. If false, tell why. Use a calculator for Exercises 39 and 42. 1 tan² 60° = sec² 60°

Determine whether each statement is true or false. If false, tell why. Use a calculator for Exercises 39 and 42. sin 42° + sin 42° = sin 84°

In Exercises 57–70, find a positive angle less than or that is coterminal with the given angle. - 38𝜋 9

Solve each problem. See Example 6. Rotating Airplane Propeller An airplane propeller rotates 1000 times per min. Find the number of degrees that a point on the edge of the propeller will rotate in 2 sec.

Convert decimal degrees to degrees, minutes, seconds, and convert degrees, minutes, seconds to decimal degrees. If applicable, round to the nearest second or the nearest thousandth of a degree. 47° 25' 11"