SOLUTION: Solve the equation on the interval 0 less than or equal to theta which is less than 2pi.
cos(2theta) + 6sin2theta = 4
Thank you!!
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Question 521115: Solve the equation on the interval 0 less than or equal to theta which is less than 2pi.
cos(2theta) + 6sin2theta = 4
Thank you!!
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I assume you mean:
\ +\ 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:
\ -\ \sin^2(\theta)\ +\ 6\sin^2(\theta)\ =\ 4)
Use the Pythagorean Identity to change the cosine term to a sine term:
\ -\ \sin^2(\theta)\ +\ 6\sin^2(\theta)\ =\ 4)
A little Algebra Music, Maestro:
\ =\ 3)
\ =\ \pm\frac{\sqrt{3}}{2})
You will find these two 
values four places on the unit circle in the interval 
John
My calculator said it, I believe it, that settles it
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