SOLUTION: Solve the equation cos⁡θ − 5cos⁡^3θ = 0 for all positive values of θ less than 360∘ . Give the answers to three significant digits in the

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Question 1068408: Solve the equation cos⁡θ − 5cos⁡^3θ = 0 for all positive values of θ less than 360∘ . Give the answers to three significant digits in the order of increasing.
Answer by ikleyn(52864) About Me  (Show Source):
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Solve the equation cos⁡θ − 5cos⁡^3θ = 0 for all positive values of θ less than 360∘ . Give the answers to three significant digits in the order of increasing.
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cos%28theta%29+-+5%2Acos%5E3%28theta%29 = 0  --->  


cos%28theta%29%2A%281-5%2Acos%5E2%28theta%29%29 = 0 --->


This equation deploys in two independent equations 


1)  cos%28theta%29 = 0  --->  theta = 90°  or  theta = 270°.


2)  1-5%2Acos%5E2%28theta%29 = 0  --->  cos%28theta%29 = +/-1%2Fsqrt%285%29 = +/- 0.447.

    The solutions are theta = acrcos%280.447%29 = 63.48°,  180°-63.48° = 116.12°, 180°+63.48° = 243.48°  and  116.12° + 180° = 296.12°.

Answer.  The solutions are  theta = 90°,  270°,  63.48°,  116.12°,  243.48°  and  296.12°.