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Problem 104
If n is an integer, n • 180° represents an integer multiple of 180°, (2n + 1) • 90° represents an odd integer multiple of 90° , and so on. Determine whether each expression is equal to 0, 1, or ―1, or is undefined. cot[n • 180°]
Problem 106
If n is an integer, n • 180° represents an integer multiple of 180°, (2n + 1) • 90° represents an odd integer multiple of 90° , and so on. Determine whether each expression is equal to 0, 1, or ―1, or is undefined. cos[n • 360°]
Problem 2
CONCEPT PREVIEW Fill in the blank(s) to correctly complete each sentence. Given tan θ = 1/cot θ , two equivalent forms of this identity are cot θ = 1/______ and tan θ . ______ = 1 .
Problem 5
CONCEPT PREVIEW Determine whether each statement is possible or impossible. sin θ = 1/2 , csc θ = 2
Problem 8
CONCEPT PREVIEW Determine whether each statement is possible or impossible. cos θ = 1.5
Problem 10
CONCEPT PREVIEW Determine whether each statement is possible or impossible. sin² θ + cos² θ = 2
Problem 13
Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1. csc θ , given that sin θ = ―3/7
Problem 16
Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1. cot θ , given that tan θ = 18
Problem 20
Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1.
sin θ , given that csc θ = √24/3
Problem 23
Use the appropriate reciprocal identity to find each function value. Rationalize denominators when applicable. See Example 1.
sin θ , given that csc θ = 1.25
Problem 25
Concept Check What is wrong with the following item that appears on a trigonometry test? "Find sec θ , given that cos θ = 3/2 . "
Problem 28
Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 2. 84°
Problem 31
Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 2.
178°
Problem 34
Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 2.
―15°
Problem 37
Determine the signs of the trigonometric functions of an angle in standard position with the given measure. See Example 2.
―345°
Problem 40
Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions. See Example 3. cos θ > 0 , sec θ > 0
Problem 43
Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions. See Example 3.
tan θ < 0 , cos θ < 0
Problem 46
Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions. See Example 3.
csc θ > 0 , cot θ > 0
Problem 50
Identify the quadrant (or possible quadrants) of an angle θ that satisfies the given conditions. See Example 3.
tan θ < 0 , cot θ < 0
Problem 54
Determine whether each statement is possible or impossible. See Example 4. sin θ = 3
Problem 57
Determine whether each statement is possible or impossible. See Example 4. tan θ = 0.93
Problem 61
Determine whether each statement is possible or impossible. See Example 4. csc θ = 100
Problem 64
Determine whether each statement is possible or impossible. See Example 4. cot θ = ―6
Problem 67
Use identities to solve each of the following. Rationalize denominators when applicable. See Examples 5–7. Find csc θ , given that cot θ = ―1/2 and θ is in quadrant IV.
Problem 71
Use identities to solve each of the following. Rationalize denominators when applicable. See Examples 5–7. Find cot θ , given that csc θ = ―1.45 and θ is in quadrant III.
Problem 73
Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7. tan θ = ―15/8 , and θ is in quadrant II .
Problem 75
Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.
sin θ = √5/7 , and θ is in quadrant I.
Problem 79
Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.
sin θ = √2/6 , and cos θ < 0
Problem 82
Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.
csc θ = ―3 , and cos θ > 0
Problem 84
Give all six trigonometric function values for each angle θ. Rationalize denominators when applicable. See Examples 5–7.
cos θ = 1