Question

sin(3 theta)=-1

Answer 1

Sine attains -1 at an angle of \(\dfrac{3\pi}{2}\), so
\[3\theta=\frac{3\pi}{2}\]

Answer 2

wait, what if it's 1, the negative one was an acident

Answer 3

In that case, the angle would be \(\dfrac{\pi}{2}\).

Answer 4

is there a way i could figure this out like if it were given to me on a test?

Answer 5

I'd suggesting memorizing the common angles associated with the unit circle and their corresponding triangles.

http://i.stack.imgur.com/r8uHr.gif

Answer 6

thanks, and turns out the answer was pie over 6, 5 pie over 6 and 3 pie over 2

Answer 7

For example, if you were given the equation
\[\cos2x=\frac{1}{2}\]
then you'll know the angle must be \(\dfrac{\pi}{3}\) or \(\dfrac{5\pi}{3}\). Then,
\[2x=\frac{\pi}{3}~~\Rightarrow~~x=\frac{\pi}{6}\\
2x=\frac{5\pi}{3}~~\Rightarrow~~x=\frac{5\pi}{6}\]

Answer 8

I finally get it! thank you so much, that unit circle seriously helped. Is there a way i could reward you on this site (newbie over here)

Answer 9

Thanks is good enough! yw