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Problem 5.RE.30c
Use the given information to find tan(x + y).
sin y = - 2/3, cos x = -1/5, x in quadrant II, y in quadrant III
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.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.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.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.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.2
For each expression in Column I, choose the expression from Column II that completes an identity.
2. csc 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.30a
Use the given information to find sin(x + y).
sin y = - 2/3 , cos x = - 1/5, x in quadrant II, y in quadrant III
Problem 5.RE.30d
Use the given information to find the quadrant of x + y.
sin y = - 2/3, cos x = -1/5 , x in quadrant II, y in quadrant III
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.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 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))