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Problem 48
Use the identities for the cosine of a sum or difference to write each expression as a trigonometric function of θ alone.
cos(90° + θ)
Problem 50
Use the identities for the cosine of a sum or difference to write each expression as a trigonometric function of θ alone.
cos(270° + θ)
Problem 52
Find cos(s + t) and cos(s - t).
cos s = - 8/17 and cos t = - 3/5, s and t in quadrant III
Problem 54
Find cos(s + t) and cos(s - t).
sin s = 2/3 and sin t = -1/3, s in quadrant II and t in quadrant IV
Problem 56
Find cos(s + t) and cos(s - t).
cos s = √2/4 and sin t = - √5/6, s and t in quadrant IV
Problem 67
Verify that each equation is an identity (Hint: cos 2x = cos(x + x).)
cos( π/2 + x) = -sin x
Problem 69
Verify that each equation is an identity (Hint: cos 2x = cos(x + x).)
cos 2x = cos² x - sin² x
Problem 71
Verify that each equation is an identity (Hint: cos 2x = cos(x + x).)
cos 2x = 1 - 2 sin² x
Problem 73
Verify that each equation is an identity (Hint: cos 2x = cos(x + x).)
cos 2x = (cot² x - 1)/(cot² x + 1)
Problem 5.42
Write each function as an expression involving functions of θ or x alone. See Example 2.
sin (3π/4 - x)
Problem 6
Match each expression in Column I with its equivalent expression in Column II.
sin 60° cos 45° - cos 60° sin 45°
Problem 8
Match each expression in Column I with its equivalent expression in Column II.
(tan (π/3) - tan (π/4))/(1 + tan (π/3) tan (π/4))
Problem 10
Find the exact value of each expression.
sin 255°
Problem 12
Find the exact value of each expression.
tan 285°
Problem 14
Find the exact value of each expression.
sin (13π/12)
Problem 16
Find the exact value of each expression.
tan (5π/12)
Problem 18
Find the exact value of each expression.
sin (π/12)
Problem 20
Find the exact value of each expression.
sin (- 5π/12)
Problem 22
Find the exact value of each expression.
tan (-7π/12)
Problem 24
Find the exact value of each expression.
sin (-13π/12)
Problem 26
Find the exact value of each expression. See Example 1.
sin 40° cos 50° + cos 40° sin 50°
Problem 28
Find the exact value of each expression. See Example 1.
sin 5π/9 cos π/18 - cos 5π/9 sin π/18 .
Problem 30
Find the exact value of each expression. See Example 1.
[tan 80° - tan(-55°)]/[ 1 + tan 80° tan(-55°)]
Problem 32
Find the exact value of each expression. See Example 1.
[tan 5π/12 + tan π/4]/[1 - tan 5π/12 tan π/4]
Problem 34
Write each function as an expression involving functions of θ or x alone. See Example 2.
cos(θ - 30°)
Problem 36
Write each function as an expression involving functions of θ or x alone. See Example 2.
cos(45° - θ)
Problem 38
Write each function as an expression involving functions of θ or x alone. See Example 2.
sin(45° + θ)
Problem 40
Write each function as an expression involving functions of θ or x alone. See Example 2.
tan (π/4 + x)
Problem 44
Write each function as an expression involving functions of θ or x alone. See Example 2.
tan(180° + θ)
Problem 46
Write each function as an expression involving functions of θ or x alone. See Example 2.
sin(π + x)
