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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.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 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.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.RE.32a
Use the given information to find sin(x + y).
cos x = 2/9, sin y = - 1, x in quadrant IV, 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.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.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..6
For each expression in Column I, choose the expression from Column II that completes an identity.
6. sec² 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 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))