Answer to Question #176966 in Trigonometry for Tony Huang

Question

Given sin a = 24/25, a in quadrant 2, and cos B = -4/5, in quadrant, find A) sin(a+B) and B) cos(a+B).

Answer 1

Given:

sin(a) = 24/25, a in 2 quadrant.

cos(b) = -4/5, b in 2 quadrant.

A) sin (a+b)

$\boxed{sin (a+b)=sin(a)cos(b)+cos(a)sin(b)}$

$sin (a+b)=({24\over25})*(-{4\over5})+(-{7\over25})({3\over5})$

$sin (a+b)=-{117\over125}$

B)cos(a+b)

$\boxed{cos(a+b)=cos(a)cos(b)-sin(a)sin(b)}$

$cos(a+b)=(-{7\over25})*(-{4\over5})-({24\over25})*({3\over5})$

$Cos(a+b)=-{44\over125}$