SOLUTION: If sine theta = 1/3, theta in Quadrant II, find sin theta + pi/6

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Question 1201608: If sine theta = 1/3, theta in Quadrant II, find sin theta + pi/6
Answer by ikleyn(52786) About Me  (Show Source):
You can put this solution on YOUR website!
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If sine theta = 1/3, theta in Quadrant II, find sin theta + pi/6
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Step 1.  If sin%28theta%29 = 1/3  and  theta in Quadrant II, then it implies

            cos%28theta%29 = -sqrt%281-sin%5E2%28theta%29%29 = -sqrt%281+-+1%2F9%29 = -sqrt%288%29%2F3 = %28-2sqrt%282%29%29%2F3.


Step 2.  sin%28theta%2Bpi%2F6%29 = sin%28theta%29%2Acos%28pi%2F6%29 + cos%28theta%29%2Asin%28pi%2F6%29 = 

         = %281%2F3%29%2A%28sqrt%283%29%2F2%29 + %28%28-2%2Asqrt%282%29%29%2F3%29%2A%281%2F2%29 = sqrt%283%29%2F6 - %282%2Asqrt%282%29%29%2F6 = %28sqrt%283%29-2%2Asqrt%282%29%29%2F6 = -0.1827 (rounded).    ANSWER

Solved.