Question 521115
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I assume you mean:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos\left(2\theta\right)\ +\ 6\sin^2\left(\theta\right)\ =\ 4]


(Note, use the caret mark (Shift-6: ^) to indicate raising to a power as in sin^2(theta))


Use the Double Angle formula for cosine:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \cos^2(\theta)\ -\ \sin^2(\theta)\ +\ 6\sin^2(\theta)\ =\ 4]


Use the Pythagorean Identity to change the cosine term to a sine term:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 1\ -\ \sin^2(\theta)\ -\ \sin^2(\theta)\ +\ 6\sin^2(\theta)\ =\ 4]


A little Algebra Music, Maestro:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4\sin^2(\theta)\ =\ 3]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \sin(\theta)\ =\ \pm\frac{\sqrt{3}}{2}]


You will find these two *[tex \Large y] values four places on the unit circle in the interval *[tex \Large 0\ <\ \theta\ <\ 2\pi]


<img src="http://www.math.ucsd.edu/~jarmel/math4c/Unit_Circle_Angles.png">


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
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