SOLUTION: Please if someone could kindly help me with this question. Thank you.
Solve for all possible x in (o, 360 degrees): 2 sin x = 2 cos 2x
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Question 623700: Please if someone could kindly help me with this question. Thank you.
Solve for all possible x in (o, 360 degrees): 2 sin x = 2 cos 2x
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ 2\cos(2x))
\ =\ \cos(2x))
Use
\ =\ \cos^2(\varphi)\ -\ \sin^2(\varphi))
To write:
\ =\ \cos^2(x)\ -\ \sin^2(x))
\ +\ \sin(x)\ =\ \cos^2(x))
Use the Pythagorean Identity
\ +\ \sin^2(\varphi)\ =\ 1)
to write:
\ +\ \sin(x)\ =\ 1\ -\ \sin^2(x))
\ +\ \sin(x)\ -\ 1\ =\ 0)
Let )
Solve the quadratic. It factors, but clumsily; the quadratic equation will be faster.
Substitute back: \ =\ u)
, giving you 2 values for )
. Find the three angles in the given interval on the unit cirle that satisfy your two values for
Hint: is the 
-coordinate.
John
My calculator said it, I believe it, that settles it
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