SOLUTION: If tan theta=3, theta is acute find sin and cos

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Question 1045410: If tan theta=3, theta is acute find sin and cos
Answer by ikleyn(52851) About Me  (Show Source):
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If tan theta=3, theta is acute find sin and cos
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You are given tan%28theta%29 = 3.


1.  Then sin%5E2%28theta%29 = tan%5E2%28theta%29%2F%281+%2B+tan%5E2%28theta%29%29 = 3%5E2%2F%281%2B3%5E2%29 = 9%2F10.


    Hence, sin%28theta%29 = +/-sqrt%289%2F10%29 = +/-3%2Fsqrt%2810%29.


    Since the angle theta is acute, the sine is positive.


    Then  sin%28theta%29 = 3%2Fsqrt%2810%29 is the only answer.


2.  cos%5E2%28theta%29 = 1%2F%281+%2B+tan%5E2%28theta%29%29 = 1%2F%281%2B3%5E2%29 = 1%2F%281%2B9%29 = 1%2F10.


    Hence, cos%28theta%29 = +/-sqrt%281%2F10%29 = +/-1%2Fsqrt%2810%29.


    Since the angle theta is acute, the cosine is positive.


    Then  cos%28theta%29 = 1%2Fsqrt%2810%29 is the only answer.