Back
Problem 5.2
Determine whether the positive or negative square root should be selected.
cos 58° = ±√ (1 + cos 116°)/2]
Problem 5.20
Use the given information to find each of the following.
sin x/2 , given cos x = - 5/8, with π/2 < x < π
Problem 5.20
Write each function value in terms of the cofunction of a complementary angle.
sin 15°
Problem 5.20
Find the exact value of each expression.
sin (- 5π/12)
Problem 5.20
Perform each indicated operation and simplify the result so that there are no quotients.
(1 + tan θ)² - 2 tan θ
Problem 5.22
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 5.22
Use the given information to find each of the following.
cos θ/2 , given sin θ = - 4/5 , with 180° < θ < 270°
Problem 5.22
Write each function value in terms of the cofunction of a complementary angle.
sin (2π/5)
Problem 5.22
Find the exact value of each expression.
tan (-7π/12)
Problem 5.22
Perform each indicated operation and simplify the result so that there are no quotients.
1/( sin α - 1) - 1/(sin α + 1)
Problem 5.24
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 300°
Problem 5.24
Use the given information to find each of the following.
cos x/2 , given cot x = -3, with π/2 < x < π
Problem 5.24
Write each function value in terms of the cofunction of a complementary angle.
sin 142° 14'
Problem 5.24
Find the exact value of each expression.
sin (-13π/12)
Problem 5.24
Factor each trigonometric expression.
sec² θ - 1
Problem 5.26
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 5.26
Use the given information to find each of the following.
cot θ/2, given tan θ = -(√5)/2 , with 90° < θ < 180°
Problem 5.26
Write each function value in terms of the cofunction of a complementary angle.
cot (9π/10)
Problem 5.26
Find the exact value of each expression. See Example 1.
sin 40° cos 50° + cos 40° sin 50°
Problem 5.26
Factor each trigonometric expression.
(tan x + cot x)² - (tan x - cot x)²
Problem 5.28
Use the given information to find sin(x + y), cos(x - y), tan(x + y), and the quadrant of x + y.
sin x = 3/5, cos y = 24/25, x in quadrant I, y in quadrant IV
Problem 5.28
Use the given information to find each of the following.
cos θ, given cos 2θ = 1/2 and θ terminates in quadrant II
Problem 5.28
Write each function value in terms of the cofunction of a complementary angle.
tan 174° 03'
Problem 5.28
Find the exact value of each expression. See Example 1.
sin 5π/9 cos π/18 - cos 5π/9 sin π/18 .
Problem 5.28
Factor each trigonometric expression.
4 tan² β + tan β - 3
Problem 5.30
Use the given information to find each of the following.
sin x, given cos 2x = 2/3 , with π < x < 3π/2
Problem 5.30
Write each function value in terms of the cofunction of a complementary angle.
sin 98.0142°
Problem 5.30
Find the exact value of each expression. See Example 1.
[tan 80° - tan(-55°)]/[ 1 + tan 80° tan(-55°)]
Problem 5.30
Factor each trigonometric expression.
cot⁴ x + 3 cot² x + 2
Problem 5.30a
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