2. Trigonometric Functions on Right Triangles

In Exercises 1–4, the graph of a tangent function is given. Select the equation for each graph from the following options: y = tan(x + π/2), y = tan(x + π), y = −tan(x − π/2).

In Exercises 1–4, the graph of a tangent function is given. Select the equation for each graph from the following options: y = tan(x + π/2), y = tan(x + π), y = −tan(x − π/2).

In Exercises 1–4, graph one period of each function. y = 2 tan x/2

In Exercises 5–12, graph two periods of the given tangent function. y = 3 tan x/4

In Exercises 5–12, graph two periods of the given tangent function. y = −2 tan 1/2 x

In Exercises 5–12, graph two periods of the given tangent function. y = tan(x − π/4)

In Exercises 13–16, the graph of a cotangent function is given. Select the equation for each graph from the following options: y = cot(x + π/2), y = cot(x + π), y = −cot x, y= −cot(x − π/2).

In Exercises 17–24, graph two periods of the given cotangent function. y = 2 cot x

In Exercises 18–24, graph two full periods of the given tangent or cotangent function. y = −2 tan π/4 x

In Exercises 17–24, graph two periods of the given cotangent function. y = 1/2 cot 2x

In Exercises 18–24, graph two full periods of the given tangent or cotangent function. y = −tan(x − π/4)

In Exercises 17–24, graph two periods of the given cotangent function. y = −3 cot π/2 x

In Exercises 18–24, graph two full periods of the given tangent or cotangent function. y = − 1/2 cot π/2 x

In Exercises 17–24, graph two periods of the given cotangent function. y = 3 cot(x + π/2)

In Exercises 45–52, graph two periods of each function. y = 2 tan(x − π/6) + 1

In Exercises 55–58, use a graph to solve each equation for -2π ≤ x ≤ 2π. tan x = -1

In Exercises 55–58, use a graph to solve each equation for -2π ≤ x ≤ 2π. csc x = 1

In Exercises 49–54, find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round answers to the nearest whole number.

In Exercises 49–54, find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round answers to the nearest whole number.

In Exercises 30–32, find the measure of the side of the right triangle whose length is designated by a lowercase letter. Round answers to the nearest whole number.

In Exercises 1–12, solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. A = 23.5°, b = 10

In Exercises 1–12, solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. A = 52.6°, c = 54

In Exercises 1–12, solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. B = 16.8°, b = 30.5

In Exercises 1–12, solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. a = 30.4, c = 50.2

In Exercises 1–12, solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. a = 10.8, b = 24.7

In Exercises 1–12, solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. b = 2, c = 7

In Exercises 29–36, find the length x to the nearest whole unit.

In Exercises 29–36, find the length x to the nearest whole unit.

In Exercises 29–36, find the length x to the nearest whole unit.

In Exercises 29–36, find the length x to the nearest whole unit.

In Exercises 54–57, solve the right triangle shown in the figure. Round lengths to two decimal places and express angles to the nearest tenth of a degree. A = 22.3°, c = 10

CONCEPT PREVIEW Match each equation in Column I with the appropriate right triangle in Column II. In each case, the goal is to find the value of x. I II 1. A. B. C. 2. 3. x = 5 tan 38° D. E. F. 4. 5. 6.

CONCEPT PREVIEW Match each equation in Column I with the appropriate right triangle in Column II. In each case, the goal is to find the value of x. I II 1. A. B. C. 2. 3. D. E. F. 4. 5. x = 5 sin 38° 6.

Concept Check Refer to the discussion of accuracy and significant digits in this section to answer the following. Mt. Everest When Mt. Everest was first surveyed, the surveyors obtained a height of 29,000 ft to the nearest foot. State the range represented by this number. (The surveyors thought no one would believe a measurement of 29,000 ft, so they reported it as 29,002.) (Data from Dunham, W., The Mathematical Universe, John Wiley and Sons.)

Concept Check Refer to the discussion of accuracy and significant digits in this section to answer the following. WNBA Scorer Women's National Basketball Association player Breanna Stewart of the Seattle Storm was the WNBA's top scorer for the 2018 regular season, with 742 points. Is it appropriate to consider this number between 741.5 and 742.5? Why or why not? (Data from www.wnba.com)

Solve each right triangle. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2.

Solve each right triangle. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2.

Solve each right triangle. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2.

Solve each right triangle. In each case, C = 90°. If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2. B = 73.0°, b = 128 in.

Solve each right triangle. In each case, C = 90°. If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2. B = 51.7°, a = 28.1 ft

Solve each right triangle. In each case, C = 90°. If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2. b = 32 ft, c = 51 ft

Solve each right triangle. In each case, C = 90°. If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2. a = 958 m, b = 489 m

Solve each right triangle. In each case, C = 90°. If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2. A = 53°24', c = 387.1 ft

Solve each right triangle. In each case, C = 90°. If angle information is given in degrees and minutes, give answers in the same way. If angle information is given in decimal degrees, do likewise in answers. When two sides are given, give angles in degrees and minutes. See Examples 1 and 2. B = 39°09', c = 0.6231 m

Solve each problem. See Examples 1–4. Distance across a Lake To find the distance RS across a lake, a surveyor lays off length RT = 53.1 m, so that angle T = 32°10' and angle S = 57°50'. Find length RS.

Solve each problem. See Examples 1–4. Diameter of the Sun To determine the diameter of the sun, an astronomer might sight with a transit (a device used by surveyors for measuring angles) first to one edge of the sun and then to the other, estimating that the included angle equals 32'. Assuming that the distance d from Earth to the sun is 92,919,800 mi, approximate the diameter of the sun.

Solve each problem. See Examples 1–4. Altitude of a Triangle Find the altitude of an isosceles triangle having base 184.2 cm if the angle opposite the base is 68°44'.

Solve each problem.See Examples 3 and 4. Distance from the Ground to the Top of a Building The angle of depression from the top of a building to a point on the ground is 32°30'. How far is the point on the ground from the top of the building if the building is 252 m high?

Solve each problem.See Examples 3 and 4. Length of a Shadow Suppose that the angle of elevation of the sun is 23.4°. Find the length of the shadow cast by a person who is 5.75 ft tall.​​

Solve each problem.See Examples 3 and 4. Angle of Depression of a Light A company safety committee has recommended that a floodlight be mounted in a parking lot so as to illuminate the employee exit, as shown in the figure. Find the angle of depression of the light to the nearest minute.

Solve each problem.See Examples 3 and 4. Angle of Elevation of the Sun The length of the shadow of a building 34.09 m tall is 37.62 m. Find the angle of elevation of the sun to the nearest hundredth of a degree.

Solve each right triangle. In Exercise 46, give angles to the nearest minute. In Exercises 47 and 48, label the triangle ABC as in Exercises 45 and 46.

Solve each right triangle. In Exercise 46, give angles to the nearest minute. In Exercises 47 and 48, label the triangle ABC as in Exercises 45 and 46. A = 39.72°, b = 38.97 m

Solve each problem. (Source for Exercises 49 and 50: Parker, M., Editor, She Does Math, Mathematical Association of America.) Height of a Tower The angle of depression from a television tower to a point on the ground 36.0 m from the bottom of the tower is 29.5°. Find the height of the tower.