6. Trigonometric Identities and More Equations

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

sin y = - 2/3, cos x = -1/5 , x in quadrant II, y in quadrant III

Write each function value in terms of the cofunction of a complementary angle.

cot (9π/10)

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

In Exercises 57–64, find the exact value of the following under the given conditions:

b. sin (α + β)

cos α = 8/17, α lies in quadrant IV, and sin β = -1/2, β lies in quadrant III.

Find cos(s + t) and cos(s - t).

sin s = 2/3 and sin t = -1/3, s in quadrant II and t in quadrant IV

Determine whether each statement is true or false. If false, tell why. See Example 4. cos(30° + 60°) = cos 30° + cos 60°

Verify that each equation is an identity.

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

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 s + t. See Example 3.

cos s = -1/5 and sin t = 3/5, s and t in quadrant II

In Exercises 57–64, find the exact value of the following under the given conditions: b. sin (α + β), sin α = 5/6 , 𝝅/2 < α < 𝝅 , and tan β = 3/7 , 𝝅 < β < 3𝝅/2 .

Find the exact value of each expression. See Example 1.

[tan 5π/12 + tan π/4]/[1 - tan 5π/12 tan π/4]

Match each expression in Column I with its equivalent expression in Column II.

(tan (π/3) - tan (π/4))/(1 + tan (π/3) tan (π/4))

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

Expand the expression using the sum & difference identities and simplify.

$\(\sin\[\left\)(-\(\theta\)-\(\frac{\pi}{2}\]\right\))$

Write each function as an expression involving functions of θ or x alone. See Example 2.

sin(π + x)