Question 925472: How do I evaluate these this two sine and cosine problems. Difficult!?
Evaluate cos(a − b) if cos a = 4/5 tan a < 0, tan b = −√15 and cos b < 0
cos(a-b) =
and
Evaluate sin(x + y) if sin x = 3/5 sec x > 0, cos y = − (2√5)/5 and tan y < 0.
sin(x + y) =
THANKS!
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! Not too difficult - use cosine addition/subtraction formulas:
cos(a-b) = cos a cos b - sin a sin b
You know cos a and the sign of tan a, so you have enough information to find sin a (hint: sin^2 a + cos^2 a = 1). You know tan b and the sign of cos b, which is enough to determine sin b and cos b (hint: also use sin^2 b + cos^2 b = 1).
The second problem is similar, except you will be using the identity sin(x+y) = sin x cos y + sin y cos x.
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