SOLUTION: I need to find the solution for d. 300=50/sin(d/2)

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Question 70757: I need to find the solution for d. 300=50/sin(d/2)
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
300=50%2Fsin%28d%2F2%29 solve for d
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Replace d/2 by A for the time being to get:
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300=50%2Fsin%28A%29
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Multiply both sides by sin(A) to get:
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300%2Asin%28A%29+=+50%2Asin%28A%29%2Fsin%28A%29
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Replace the sin(A)/sin(A) by 1. As a result the equation is:
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300%2Asin%28A%29+=+50
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Divide both sides by 300 and get:
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sin%28A%29+=+50%2F300+=+1%2F6
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Now by taking the arcsin(A) = 1/6 on a calculator you find that A = 9.5941 degrees.
But before we had decided that A=d%2F2. Therefore d = A*2. If we substitute 9.5941
degrees for A we get that d = 9.5941*2 = 19.0982 degrees.
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This is a principal solution. It can be converted to radians by multiplying 19.0982
degrees by pi%2F180.
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Don't forget that sin(A) is also positive in the second quadrant. Therefore, the angle
170.4059 degrees is also a possible solution for A in sin(A) = 1/6. And since A+=+d%2F2
we can write 170.4059 degrees = d/2. Solving for d we get 340.8118 degrees.
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Again these answers in degrees can be converted to radians by multiplying by pi%2F180.
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Hopefully this gives you a clue as to how to work this problem.