# SOLUTION: Find all solutions for the equation. Record your answers in exact form where possible. 2 cos ^2 x = -3sin x Thanks for your help, any help is appreciated

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: Find all solutions for the equation. Record your answers in exact form where possible. 2 cos ^2 x = -3sin x Thanks for your help, any help is appreciated       Log On

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 Algebra: Trigonometry Solvers Lessons Answers archive Quiz In Depth

 Question 324020: Find all solutions for the equation. Record your answers in exact form where possible. 2 cos ^2 x = -3sin x Thanks for your help, any help is appreciated Answer by solver91311(16868)   (Show Source): You can put this solution on YOUR website! First thing to do is remember that Which means that you can re-cast your equation thus: and then a little re-arranging: Next, let , so: which factors rather tidily: Hence or But recall that . Since the range of is , we must exclude . Therefore: Finally, Looking at the unit circle and remembering that sin is the -coordinate of a point on the unit circle, (see http://en.wikipedia.org/wiki/Unit_circle) You see that there are two possibilities, or . However, the instructions for the problem say to find all solutions and does not give a range, hence we need to allow for the periodicity of the sine function. Therefore the final answer is: or where John