If cos α = 0.587 and sin β = 0.146 with both angles’ terminal rays in Quadrant-I, find the values of (a) cos ( α + β ) = (b) sin ( α − β ) =

Answer 1

a)

cos(α+β) = cos(α)cos(β) - sin(α)sin(β)

Need sin(α) and cos(β)

cos(α) = 587/1000 = x/h y = √(h²-x²) = √(1000000 - 344569) = 809.6

sin(α) = 809.6/1000 = 0.8096

sin(β) = 146/1000 = y/h x = √(h²-y²) = √(1000000 - 21316) = 989,3

cos(β) = 989.3/1000 = 0.9893

Now it's just math left for you to solve.

b) sin(α-β) = sin(α)cos(β) - sin(β)cos(α)

Just plug in the values for the sine's and cosine's to solve.