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How do I write sin x in terms of cos x? 

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alyssa2014chica | Student, Grade 10 | eNotes Newbie

Posted May 14, 2012 at 11:06 PM via web

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How do I write sin x in terms of cos x? 

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted May 15, 2012 at 7:13 AM (Answer #1)

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To write sin x in terms of cos x use the relation `sin^2x + cos^2x=1`

=> `sin^2x = 1 - cos^2x`

Taking the square root of both the sides gives two values of sin x

`sin x = sqrt(1 - cos^2x)` and `sin x = -sqrt(1 - cos^2x)` . This makes it essential to know in which quadrant the angle x lies so that it can be determined if the value of sin x is positive or negative.

`sin x = sqrt(1 - cos^2x)` or `sin x = -sqrt(1 - cos^2x)`  depending on which quadrant x lies in.

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