SOLUTION: Solve: 4 sin x = csc x

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Question 114301This question is from textbook Precalculus with Limits
: Solve:
4 sin x = csc x This question is from textbook Precalculus with Limits

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1: Remember that csc%28x%29=1%2Fsin%28x%29

Step 2: Substitute

4%2Asin%28x%29=1%2Fsin%28x%29, then multiply both sides by sin%28x%29
4%2Asin%5E2%28x%29=1, then take the square root
sqrt%284%2Asin%5E2%28x%29%29=%2Bsqrt%281%29 or sqrt%284%2Asin%5E2%28x%29%29=-sqrt%281%29
2%2Asin%28x%29=1 or 2%2Asin%28x%29+=+-1
sin%28x%29=1%2F2 or sin%28x%29=-1%2F2
x=arcsin%281%2F2%29 => x=pi%2F6 or x=5%2Api%2F6, or x=arcsin%28-1%2F2%29 => x=7%2Api%2F6 or x=11%2Api%2F6

Hope that helps,
John