Textbook Question
Determine whether each statement is possible or impossible. See Example 4. sin θ = 3
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Ch. 1 - Trigonometric Functions
Lial12th EditionTrigonometryISBN: 9780136552161
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Table of contents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Chapter 2, Problem 52
Perform each calculation. See Example 3. 55° 30' + 12° 44' ― 8° 15'
Verified step by step guidance1
First, separate the degrees and minutes for each angle: 55° 30', 12° 44', and 8° 15'.
Add the degrees and minutes of the first two angles: add 55° and 12° for degrees, and 30' and 44' for minutes.
If the sum of the minutes is 60 or more, convert 60 minutes into 1 degree and add it to the degrees sum, then subtract 60 from the minutes sum.
Next, subtract the third angle (8° 15') from the result obtained in the previous step by subtracting degrees and minutes separately.
If the minutes in the subtraction step are negative, borrow 1 degree (which equals 60 minutes) from the degrees part, add 60 to the minutes, and then perform the subtraction.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Angle Measurement in Degrees and Minutes
Angles can be expressed in degrees (°) and minutes ('). One degree equals 60 minutes, similar to how time is measured. Understanding this notation is essential for performing accurate calculations involving angles.
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Reference Angles on the Unit Circle
Addition and Subtraction of Angles
When adding or subtracting angles, degrees and minutes must be handled separately. If the minutes exceed 60, convert the excess into degrees. Similarly, if subtracting results in negative minutes, borrow one degree to adjust the minutes.
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3:18Adding and Subtracting Complex Numbers
Borrowing and Carrying in Angle Calculations
Borrowing and carrying are techniques used to manage minutes during addition or subtraction. For example, if minutes sum to more than 60, carry over the extra 60 minutes as one degree. If minutes are insufficient during subtraction, borrow one degree (60 minutes) to complete the operation.
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04:46Coterminal Angles
Related Practice
Textbook Question
Concept Check Suppose that the point (x, y) is in the indicated quadrant. Determine whether the given ratio is positive or negative. Recall that r = √(x² + y²) .(Hint: Drawing a sketch may help.) I , r/y
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Textbook Question
Perform each calculation. See Example 3. 90° ― 36° 18' 47"
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Textbook Question
An equation of the terminal side of an angle θ in standard position is given with a restriction on x. Sketch the least positive such angle θ , and find the values of the six trigonometric functions of θ . See Example 3. ―5x ― 3y = 0 , x ≤ 0
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Textbook Question
Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. See Example 4(a). 82° 30'
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Textbook Question
An equation of the terminal side of an angle θ in standard position is given with a restriction on x. Sketch the least positive such angle θ , and find the values of the six trigonometric functions of θ . See Example 3. 2x + y = 0 , x ≥ 0
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