6. Trigonometric Identities and More Equations

Use the given information to find tan(x + y).

cos x = 2/9, sin y = -1/2, x in quadrant IV, y in quadrant III

Use the given information to find the quadrant of x + y.

cos x = 2/9, sin y = -1/2, x in quadrant IV, y in quadrant III

Verify that each equation is an identity.

sin(x + y) + sin(x - y) = 2 sin x cos y

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)

Verify that each equation is an identity.

sin(s + t)/cos s cot t = tan s + tan t

Verify that each equation is an identity.

sin(x + y)/cos(x - y) = (cot x + cot y)/(1 + cot x cot y)

Verify that each equation is an identity.

(tan(α + β) - tan β)/(1 + tan(α + β) tan β) = tan α

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

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

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

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

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

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

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

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