SOLUTION: if sin theta=(1/4), theta in quadrant II, find the exact value of cos(theta+pi/6)

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Question 584605: if sin theta=(1/4), theta in quadrant II, find the exact value of cos(theta+pi/6)
Answer by lwsshak3(11628) About Me  (Show Source):
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if sin theta=(1/4), theta in quadrant II, find the exact value of cos(theta+pi/6)
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Using cos addition formula:
use x for theta
cos(x+π/6)=cosx*cos(π/6)-sinx*sin(π/6)
sinx=1/4
cosx=√15/4
cos(π/6)=√3/2
sin(π/6)=1/2
cos(x+π/6)=(√15/4*√3/2)-(1/4*1/2)
cos(x+π/6)=(√45/8)-(1/8 )
cos(x+π/6)=(√45-1)/8)