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Problem 5.10
Find values of the sine and cosine functions for each angle measure.
2x, given tan x = 5/3 and sin x < 0
Problem 5.10
Use identities to write each expression in terms of sin θ and cos θ, and then simplify so that no quotients appear and all functions are of θ only.
csc θ - sin θ
Problem 5.10
Match each expression in Column I with its value in Column II.
10. cos 67.5°
Problem 5.10
Find the exact value of each expression. (Do not use a calculator.)
cos(-15°)
Problem 5.10
Find the exact value of each expression.
sin 255°
Problem 5.12
Find values of the sine and cosine functions for each angle measure.
2θ, given cos θ = (√3)/5 and sin θ > 0
Problem 5.12
Use identities to write each expression in terms of sin θ and cos θ, and then simplify so that no quotients appear and all functions are of θ only.
csc² θ + sec² θ
Problem 5.12
Use a half-angle identity to find each exact value.
sin 195°
Problem 5.12
Find the exact value of each expression. (Do not use a calculator.)
cos 105° (Hint: 105° = 60° + 45°)
Problem 5.12
Find the exact value of each expression.
tan 285°
Problem 5.12
Perform each indicated operation and simplify the result so that there are no quotients.
sec x/csc x + csc x/sec x
Problem 5.14
Find values of the sine and cosine functions for each angle measure.
θ, given cos 2θ = 3/4 and θ terminates in quadrant III
Problem 5.14
Work each problem.
Given tan x = -5⁄4, where π/2< x < π, use the trigonometric identities to find cot x, csc x and sec x.
Problem 5.14
Use a half-angle identity to find each exact value.
cos 195°
Problem 5.14
Find the exact value of each expression. (Do not use a calculator.)
cos π/12
Problem 5.14
Find the exact value of each expression.
sin (13π/12)
Problem 5.14
Perform each indicated operation and simplify the result so that there are no quotients.
cos β(sec β + csc β)
Problem 5.16
Find values of the sine and cosine functions for each angle measure.
θ, given cos 2θ = 2/3 and 90° < θ <180°
Problem 5.16
Work each problem.
Find the exact values of sin x, cos x, and tan x, for x = π/12 , using
a. difference identities
b. half-angle identities.
Problem 5.16
Use a half-angle identity to find each exact value.
sin 165°
Problem 5.16
Find the exact value of each expression. (Do not use a calculator.)
cos (-7π/12)
Problem 5.16
Find the exact value of each expression.
tan (5π/12)
Problem 5.16
Perform each indicated operation and simplify the result so that there are no quotients.
cos x/sec x + sin x/csc x
Problem 5.18
For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.
sin 35°
Problem 5.18
The half-angle identity
tan A/2 = ± √[(1 - cosA)/(1 + cos A)]
can be used to find tan 22.5° = √(3 - 2√2), and the half-angle identity
tan A/2 = sin A/(1 + cos A)
can be used to find tan 22.5° = √2 - 1. Show that these answers are the same, without using a calculator. (Hint: If a > 0 and b > 0 and a² = b², then a = b.)
Problem 5.18
Find the exact value of each expression. (Do not use a calculator.)
cos (7π/9) cos (2π/9) - sin (7π/9) sin (2π/9)
Problem 5.18
Find the exact value of each expression.
sin (π/12)
Problem 5.18
Perform each indicated operation and simplify the result so that there are no quotients.
(tan x + cot x)²
Problem 5.20
For each expression in Column I, use an identity to choose an expression from Column II with the same value. Choices may be used once, more than once, or not at all.
-sin 35°
Problem 5.2
For each expression in Column I, choose the expression from Column II that completes an identity.
2. csc x = ____
