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 #