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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
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 5.1.34
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
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 5.1.72
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.
cos θ (cos θ - sec θ)
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 12
Perform each indicated operation and simplify the result so that there are no quotients.
sec x/csc x + csc x/sec x
Problem 14
Perform each indicated operation and simplify the result so that there are no quotients.
cos β(sec β + csc β)
Problem 16
Perform each indicated operation and simplify the result so that there are no quotients.
cos x/sec x + sin x/csc x
Problem 18
Perform each indicated operation and simplify the result so that there are no quotients.
(tan x + cot x)²
Problem 88
Verify that each equation is an identity.
sin³ θ + cos³ θ = (cos θ + sin θ) (1 - cos θ sin θ)
Problem 5.10
Find the exact value of each expression. (Do not use a calculator.)
cos(-15°)
Problem 12
Find the exact value of each expression. (Do not use a calculator.)
cos 105° (Hint: 105° = 60° + 45°)
Problem 14
Find the exact value of each expression. (Do not use a calculator.)
cos π/12
Problem 16
Find the exact value of each expression. (Do not use a calculator.)
cos (-7π/12)
Problem 18
Find the exact value of each expression. (Do not use a calculator.)
cos (7π/9) cos (2π/9) - sin (7π/9) sin (2π/9)
Problem 20
Write each function value in terms of the cofunction of a complementary angle.
sin 15°
Problem 22
Write each function value in terms of the cofunction of a complementary angle.
sin (2π/5)
Problem 24
Write each function value in terms of the cofunction of a complementary angle.
sin 142° 14'
Problem 26
Write each function value in terms of the cofunction of a complementary angle.
cot (9π/10)
Problem 28
Write each function value in terms of the cofunction of a complementary angle.
tan 174° 03'
Problem 30
Write each function value in terms of the cofunction of a complementary angle.
sin 98.0142°
Problem 32
Use identities to fill in each blank with the appropriate trigonometric function name.
sin 2π/3 = _____ (- π/6)
Problem 34
Use identities to fill in each blank with the appropriate trigonometric function name.
____ 72° = cot 18°
Problem 36
Use identities to fill in each blank with the appropriate trigonometric function name.
tan 24° = 1/ _____ 66°
Problem 37
Find one value of θ or x that satisfies each of the following.
tan θ = cot(45° + 2θ)
Problem 38
Find one value of θ or x that satisfies each of the following.
sin θ = cos(2θ + 30°)
Problem 39
Find one value of θ or x that satisfies each of the following.
sec x = csc (2π/3)
Problem 40
Find one value of θ or x that satisfies each of the following.
cos x = sin (π/12)
Problem 44
Use the identities for the cosine of a sum or difference to write each expression as a trigonometric function of θ alone.
cos(90° - θ)
Problem 46
Use the identities for the cosine of a sum or difference to write each expression as a trigonometric function of θ alone.
cos(θ - 270°)