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Question

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anonymous · Answer

$$\sin^{-1}(\cos \frac{2\pi}{3})$$
Start inside.
What's the cosine of 2pi/3?

anonymous · Answer

.999

anonymous · Answer

or -1/2?

anonymous · Answer

Yes.  -1/2.
So now do the next part!

anonymous · Answer

sin of -1/2.. so 7pi/6?

anonymous · Answer

or 11pi/6?

anonymous · Answer

$$-\pi/6$$
I think that might be equivalent but I don't remember enough trig to be sure.

anonymous · Answer

where did the neg pi/6 come from...

anonymous · Answer

A complete circle is $$12\pi/6$$
So 11 and -1 are the same. You're going "backwards" 1/6pi.

anonymous · Answer

k

zepdrix · Answer

$$\Large \sin^{-1}\left[-\frac{1}{2}\right]$$So you were probably thinking to yourself that this should produce 7pi/6 or 11pi/6.

Arcsine is only defined in the 1st and 4th quadrant so we use the 4th quadrant angle for this result! :)

anonymous · Answer

so 11pi/6 so 330 degrees is answer?

zepdrix · Answer

Ummm yah that sounds right.

watchmath · Answer

Let $\theta =\sin^{-1}(\cos (2\pi/3))$. Then $\sin \theta=\cos (2\pi/3)=-\frac{1}{2}$. Since $\theta \in [-\pi/2,\pi/2]$ (which is the range of the sine inverse) then $\theta =-\pi/6$

zepdrix · Answer

Oh goodness I'm such a doofus +_+ I said 11pi/6 lol...
refer to watchmath's post for the correct answer :P

anonymous · Answer

Thanks! That's the kind of stuff I didn't remember.