document.write( "Question 921612: if cos theta = 1/4 in quadrant IV find the exact value of sin( theta - pi/4) \n" ); document.write( "
Algebra.Com's Answer #559124 by lwsshak3(11628)\"\" \"About 
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if cos theta = 1/4 in quadrant IV find the exact value of sin( theta - pi/4)
\n" ); document.write( "use x for theta
\n" ); document.write( "cosx=1/4
\n" ); document.write( "sinx=-√(1-cos^2x)=-√(1-1/16)=-√15/16=-√15/4
\n" ); document.write( "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
\n" ); document.write( "note: in quadrant IV cos>0, sin<0.
\n" ); document.write( "..
\n" ); document.write( "calculator check: (set calculator to radians)
\n" ); document.write( "cosx=1/4
\n" ); document.write( "x≈4.965 (radians)(in quadrant IV)
\n" ); document.write( "x-π/4≈4.1797
\n" ); document.write( "sin(x-π/4)≈sin(4.1797)≈-0.8614
\n" ); document.write( "exact value=-(√30+√2)/8≈-0.8614
\n" ); document.write( "..
\n" ); document.write( "note to student:
\n" ); document.write( "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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