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Problem 5.RE.8
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.
cot(-θ)/sec(-θ)
Problem 5.RE.40
Use the given information to find each of the following.
sin y, given cos 2y = -1/3 , π/2 < y < π
Problem 5.RE.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.RE.4
For each expression in Column I, choose the expression from Column II that completes an identity.
4. cot x = ____
II
A. sin ^2 x/cos ^2 x
B.1/(sec ^2 x)
C. sin (-x)
D. csc ^2 x-cot ^2 x + sin ^2 x
E. tan x
Problem 5.RE.42
Use the given information to find each of the following.
sin 2x, given sin x = 0.6, π/2 < y < π
Problem 5.RE.22
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.
cos 75°
Problem 5.RE.26
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.
cos(-55°)
Problem 5.RE.32d
Use the given information to find the quadrant of x + y.
cos x = 2/9, sin y = -1/2, x in quadrant IV, y in quadrant III
Problem 5.RE.30b
Use the given information to find cos(x - y).
sin y = - 2/3, cos x = -1/5, x in quadrant II, y in quadrant III
Problem 5.RE.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.RE.32c
Use the given information to find tan(x + y).
cos x = 2/9, sin y = -1/2, x in quadrant IV, y in quadrant III
Problem 50
Verify that each equation is an identity.
2 cos³ x - cos x = (cos² x - sin² x)/sec x
Problem 52
Verify that each equation is an identity.
(sin 2x)/(sin x) = 2/sec x
Problem 54
Verify that each equation is an identity.
(2 tan B)/(sin 2B) = sec² B
Problem 56
Verify that each equation is an identity.
(2 cot x)/(tan 2x) = csc² x - 2
Problem 58
Verify that each equation is an identity.
csc A sin 2A - sec A = cos 2A sec A
Problem 60
Verify that each equation is an identity.
2 cos² θ - 1 = (1 - tan² θ)/(1 + tan² θ)
Problem 62
Verify that each equation is an identity.
sec² α - 1 = (sec 2α - 1)/(sec 2α + 1)
Problem 64
Verify that each equation is an identity.
sin³ θ = sin θ - cos² θ sin θ
Problem 66
Verify that each equation is an identity.
2 cos² (x/2) tan x = tan x+ sin x
Problem 68
Verify that each equation is an identity.
(1/2)cot (x/2) - (1/2) tan (x/2) = cot x
Problem 70
Verify that each equation is an identity.
(sin 3t + sin 2t)/(sin 3t - sin 2t ) = tan (5t/2)/(tan (t/2))