If cos α = 0.902 and sin β = 0.557 with both angles’ terminal rays in Quadrant-I, find the values of (a) cos ( α + β ) = (b) cos ( β − α ) =

Answer 1

I find angle α = cos^-1 (0.902) = 25.58^° and β = sin^-1 (0.557) = 33.85^°. Then use sum and difference identities:

a) cos(α+β) = cos α cos β - sin α sin β = (0.902)(0.8305) - (0.4317)(0.557) = 0.509 [check: = cos(59.4)].

b) cos(β-α) = cos β cos α + sin β sin α = (0.8305)(0.902) + (0.557)(0.4317) = 0.990 [check: = cos(8.3)].