Find the Exact Values

Question

Find the exact value (Do not use a calculator) of each expression using reference triangles, Addition and Subtraction Formulas, Double Angle Formulas, and/or Half-Angle Formulas under the given conditions.

Given: sin alpha= -1/5, alpha in quadrant III and cos beta= 1/5, beta in quadrant IV

Find:

a. sin (alpha + beta)

b. cos (alpha-beta)

Answer 1

sin α = -1/5, cos α = 2√6 / 5

sin β = 1/5, cos β = -2√6 / 5

a. sum formula for sine

b. difference formula for cosine