SOLUTION: find cos(s+t) given that sin s=-1/2, with s in quadrant IV, and sin t=1/4 in quadrant II

Question 927049: find cos(s+t) given that sin s=-1/2, with s in quadrant IV, and sin t=1/4 in quadrant II
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
find cos(s+t) given that sin s=-1/2, with s in quadrant IV, and sin t=1/4 in quadrant II
***
sin s=-1/2
s=11π/6
cos s=√3/2
sin t=1/4
cos t=-√(1-sin^2(t))=-√(1-1/16)=-√(15/16)=-√15/4
..
cos(s+t)=cos s*cos t-sin s*sin t=√3/2*-√15/4--1/2*1/4=-√45/8+1/8=(-√45+1)/8
check:
s=11π/6=330˚
sin t=1/4
t≈165.52˚
s+t=495.52
cos(s+t)≈cos(495.52˚)≈-0.7135
exact value as computed=(-√45+1)/8≈0.7135
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