SOLUTION: If sin θ = 2 over 7 and tan θ > 0, what is the value of cos θ? I need to show work

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Question 1042537: If sin θ = 2 over 7 and tan θ > 0, what is the value of cos θ?
I need to show work
Answer by ikleyn(52858) About Me  (Show Source):
You can put this solution on YOUR website!
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If sin (theta) = 2 over 7 and tan (theta) > 0, what is the value of cos (theta)?
I need to show work
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You are given sin%28theta%29 = 2%2F7.


Then cos%28theta%29 = sqrt%281-sin%5E2%28theta%29%29 = sqrt%281-%282%2F7%29%5E2%29 = sqrt%281+-+4%2F49%29 = sqrt%28%2849-4%29%2F49%29 = sqrt%2845%2F49%29 = %283%2Asqrt%285%29%29%2F7.


Since sin%28theta%29 is positive and tan%28theta%29 is positive (given !), the angle theta is in the first quadrant.


Since theta is in QI, the sign at the square root is positive.

Answer.  sin%28theta%29 = %283%2Asqrt%285%29%29%2F7.

Solved.