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Problem 5.RE.32b
Use the given information to cos(x - y).
cos x = 2/9, sin y = -1/2, x in quadrant IV, y in quadrant III
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.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.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.RE.36
Find values of the sine and cosine functions for each angle measure.
2y, given sec y = -5/3, sin y > 0
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.48
Graph each expression and use the graph to make a conjecture, predicting what might be an identity. Then verify your conjecture algebraically.
csc x - cot x
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 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.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.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.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 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))