Question 921612: if cos theta = 1/4 in quadrant IV find the exact value of sin( theta - pi/4)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! if cos theta = 1/4 in quadrant IV find the exact value of sin( theta - pi/4)
use x for theta
cosx=1/4
sinx=-√(1-cos^2x)=-√(1-1/16)=-√15/16=-√15/4
sin(x-π/4)=sinxcos(π/4)-cosxsin(π/4)=-√15/4*√2/2-1/4*√2/2=-√30/8-√2/8=-(√30+√2)/8
note: in quadrant IV cos>0, sin<0.
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calculator check: (set calculator to radians)
cosx=1/4
x≈4.965 (radians)(in quadrant IV)
x-π/4≈4.1797
sin(x-π/4)≈sin(4.1797)≈-0.8614
exact value=-(√30+√2)/8≈-0.8614
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note to student:
Please let me know if my solution is understandable and helpful. Of all the solutions I have submitted, I receive the least number of responses from students with trig problems.
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