Question

Solve sin2θ = 3cos2θ

Answer 1

i believe the answer is pi/3+2pin,2pi/3+2pin,4pi/3+2pin,5pi/3+2pin

Answer 2

Solve sin^2θ = 3cos^2θ

Answer 3

oh those are not double angles
?

Answer 4

no squared, didnt realize the format change

Answer 5

\[\sin^2(\theta)=1-\cos^2(\theta) \]
Therefore,
\[1-\cos^2(\theta)=3\cos^2(\theta)\]
get all the cos^2 's on one side and it will make more sense

Answer 6

\[1=4\cos^2(\theta) \\ \frac{1}{4}=\cos^2(\theta)\]

Answer 7

did you get to that equation I have there?

Answer 8

which is 1.0471975511965977461542144610932, or pi/3. Because it is squared and negatives dont matter i should be able to add pi to that formula as many times as i want. I also should be able to subtract it from two pi. therefore the possible answers are pi/3+pin. and 5pi/3 + pin. However neither of those are options, only solutions involving two pi, so pi/3+2pin,2pi/3+2pin,4pi/3+2pin,5pi/3+2pin is the correct answer, right?

Answer 9

yeah
\[\cos(\theta)=\frac{1}{2} \text{ gives us } \theta=\frac{\pi}{3} +2npi , \theta=\frac{5\pi}{3}+2npi \\ \cos(\theta)=\frac{-1}{2} \text{ gives us } \theta=\frac{2\pi}{3}+2n \pi, \theta=\frac{4\pi}{3}+2npi\]
this can be found on the unit circle though

Answer 10

Ok thanks:) yeah the subtract from two pi thing is what i meant for "found on the unit circle"

Answer 11

like we just look for when the x coordinate is 1/2 for the first one
and for the second one just look for when the x coordinate is -1/2

Answer 12

http://www.mathsisfun.com/geometry/unit-circle.html