Find the exact value of cos​(alpha minus beta​) if sin alpha equals 0.5276 and cos beta equals 0.3488​, and both alpha and beta are​ first-quadrant angles?

1 Answer
Mar 22, 2018

The exact value:
cos​(alpha - beta​) = sqrt 0.72163824 xx 0.3488 + 0.5276 xx sqrt 0.87833856

To four digits: cos​(alpha - beta​) ≈ 0.7908

Explanation:

cos​(alpha - beta​)
sin alpha = 0.5276
cos beta =0.3488​

sin^2 α + cos^2 α = 1
0.5276^2 + cos^2 α = 1
cos^2 α = 1 - 0.5276^2
cos α = + sqrt 0.72163824

sin^2 β + cos^2 β = 1
sin^2 β + 0.3488^2 = 1
sin^2 β = 1 - 0.3488^2
sin^2 β = 0.87833856
sin β = +sqrt 0.87833856

cos​(alpha - beta​) = cosα cosβ+sinα sinβ
cos​(alpha - beta​) = sqrt 0.72163824 xx 0.3488 + 0.5276 xx sqrt 0.87833856