Back
Problem 52a
Use the given information to find sin(s + t). See Example 3.
sin s = 3/5 and sin t = -12/13, s in quadrant I and t in quadrant III
Problem 52b
Use the given information to find tan(s + t). See Example 3.
sin s = 3/5 and sin t = -12/13, s in quadrant I and t in quadrant III
Problem 52c
Use the given information to find the quadrant of s + t. See Example 3.
sin s = 3/5 and sin t = -12/13, s in quadrant I and t in quadrant III
Problem 54a
Use the given information to find sin(s + t). See Example 3.
cos s = -15/17 and sin t = 4/5, s in quadrant II and t in quadrant I
Problem 54b
Use the given information to find tan(s + t). See Example 3.
cos s = -15/17 and sin t = 4/5, s in quadrant II and t in quadrant I
Problem 54c
Use the given information to find the quadrant of s + t. See Example 3.
cos s = - 15/17 and sin t = 4/5, s in quadrant II and t in quadrant I
Problem 56a
Use the given information to find sin(s + t). See Example 3.
cos s = -1/5 and sin t = 3/5, s and t in quadrant II
Problem 56b
Use the given information to find tan(s + t). See Example 3.
cos s = -1/5 and sin t = 3/5, s and t in quadrant II
Problem 56c
Use the given information to find the quadrant of s + t. See Example 3.
cos s = -1/5 and sin t = 3/5, s and t in quadrant II
Problem 62
Verify that each equation is an identity.
sin(x + y) + sin(x - y) = 2 sin x cos y
Problem 64
Verify that each equation is an identity. See Example 4.
tan(x - y) - tan(y - x) = 2(tan x - tan y)/(1 + tan x tan y)
Problem 66
Verify that each equation is an identity.
sin(s + t)/cos s cot t = tan s + tan t
Problem 68
Verify that each equation is an identity.
sin(x + y)/cos(x - y) = (cot x + cot y)/(1 + cot x cot y)
Problem 70
Verify that each equation is an identity.
(tan(α + β) - tan β)/(1 + tan(α + β) tan β) = tan α
Problem 81
Use the result from Exercise 80 to find the acute angle between each pair of lines. (Note that the tangent of the angle will be positive.) Use a calculator, and round to the nearest tenth of a degree.
x + y = 9, 2x + y = -1
Problem 82
Use the result from Exercise 80 to find the acute angle between each pair of lines. (Note that the tangent of the angle will be positive.) Use a calculator, and round to the nearest tenth of a degree.
5x - 2y + 4 = 0, 3x + 5y = 6
Problem 4
Match each expression in Column I with its value in Column II.
cos² (π/6) - sin² (π/6)
Problem 6
Match each expression in Column I with its value in Column II.
(2 tan (π/3))/(1 - tan² (π/3))
Problem 8
Find values of the sine and cosine functions for each angle measure.
2θ, given cos θ = -12/13 and sin θ > 0
Problem 10
Find values of the sine and cosine functions for each angle measure.
2x, given tan x = 5/3 and sin x < 0
Problem 12
Find values of the sine and cosine functions for each angle measure.
2θ, given cos θ = (√3)/5 and sin θ > 0
Problem 14
Find values of the sine and cosine functions for each angle measure.
θ, given cos 2θ = 3/4 and θ terminates in quadrant III
Problem 16
Find values of the sine and cosine functions for each angle measure.
θ, given cos 2θ = 2/3 and 90° < θ <180°
Problem 38
Simplify each expression. See Example 4.
2 tan 15°/(1 - tan² 15°)
Problem 40
Simplify each expression. See Example 4.
1 - 2 sin² 22 ½°
Problem 42
Simplify each expression. See Example 4.
cos² π/8 - 1/2
Problem 44
Simplify each expression. See Example 4.
tan 34°/2(1 - tan² 34°)
Problem 46
Simplify each expression. See Example 4.
⅛ sin 29.5° cos 29.5°
Problem 48
Simplify each expression. See Example 4.
cos² 2x - sin² 2x
Problem 50
Express each function as a trigonometric function of x. See Example 5.
cos 3x