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Problem 5.1.34
Find the remaining five trigonometric functions of θ.
csc θ = -5/2, θ in quadrant III
Problem 5.1.39
For each expression in Column I, choose the expression from Column II that completes an identity. One or both expressions may need to be rewritten.
-tan x cos x
Problem 5.1.76
Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.
tan(-θ)/sec θ
Problem 5.1.70
Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.
(sin θ - cos θ) (csc θ + sec θ)
Problem 5.1.68
Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.
csc θ - sin θ
Problem 5.1.30
Identify the basic trigonometric function graphed, and determine whether it is even or odd.
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Problem 5.1.54
Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.
tan θ cos θ
Problem 5.1.10
Use identities to correctly complete each sentence.
If sin θ = ⅔, then -sin(-θ) = ________________.
Problem 5.1.56
Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.
csc θ cos θ tan θ
Problem 5.1.38
Find the remaining five trigonometric functions of θ.
cos θ = -1/4, sin θ > 0
Problem 5.1.41
For each expression in Column I, choose the expression from Column II that completes an identity. One or both expressions may need to be rewritten.
sec x/csc x
Problem 5.1.62
Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.
(sec θ - 1) (sec θ + 1)
Problem 5.1.12
Find sin θ.
cos θ = 5/6, θ in quadrant I
Problem 5.1.58
Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.
sin θ sec θ
Problem 5.1.22
Find sinθ.
csc θ = -8/5
Problem 5.1.20
Find sinθ.
sec θ = 7/2, tan θ < 0
Problem 5.1.43
For each expression in Column I, choose the expression from Column II that completes an identity. One or both expressions may need to be rewritten.
cos² x
Problem 5.1.14
Find sinθ.
cot θ = -1/3, θ in quadrant IV
Problem 5.1.32
Find the remaining five trigonometric functions of θ.
cos θ = 1/5, θ in quadrant I
Problem 5.1.28
Identify the basic trigonometric function graphed, and determine whether it is even or odd.
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Problem 5.1.50
Perform each transformation. See Example 2.
Write cot x in terms of csc x.
Problem 5.1.9
Use identities to correctly complete each sentence.
If cos θ = 0.8 and sin θ = 0.6, then tan(-θ) = ________________.
Problem 5.1.52
Perform each transformation. See Example 2.
Write sec x in terms of sin x.
Problem 5.1.64
Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.
1 + cot(-θ)/cot(-θ)
Problem 5.1.74
Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.
(sec²θ - 1)/(csc²θ - 1)
Problem 5.1.36
Find the remaining five trigonometric functions of θ.
sin θ = -4/5, cos θ < 0
Problem 5.1.18
Find sinθ.
tan θ = -(√7)/2, sec θ > 0
Problem 5.1.60
Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.
cot² θ(1 + tan² θ)
Problem 5.1.66
Write each expression in terms of sine and cosine, and then simplify the expression so that no quotients appear and all functions are of θ only. See Example 3.
[1 - sin²(-θ)]/[1 + cot²(-θ)]