Question 1068408
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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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<pre>
{{{cos(theta) - 5*cos^3(theta)}}} = 0  --->  


{{{cos(theta)*(1-5*cos^2(theta))}}} = 0 --->


This equation deploys in two independent equations 


1)  {{{cos(theta)}}} = 0  --->  {{{theta}}} = 90°  or  {{{theta}}} = 270°.


2)  {{{1-5*cos^2(theta)}}} = 0  --->  {{{cos(theta)}}} = +/-{{{1/sqrt(5)}}} = +/- 0.447.

    The solutions are {{{theta}}} = {{{acrcos(0.447)}}} = 63.48°,  180°-63.48° = 116.12°, 180°+63.48° = 243.48°  and  116.12° + 180° = 296.12°.
</pre>

<U>Answer</U>. &nbsp;The solutions are &nbsp;{{{theta}}} = 90°, &nbsp;270°, &nbsp;63.48°,  &nbsp;116.12°, &nbsp;243.48°  &nbsp;and  &nbsp;296.12°.