Help with

Tan^-1(sin(2pi/3))

Question

Help with 

Tan^-1(sin(2pi/3))

anonymous · Answer

Draw the right triangle.

anonymous · Answer

Make sure you notice which quadrant 2π/3 is in.

p0sitr0n · Answer

sin(2pi/3)=2sin(pi/3)cos(pi3)

p0sitr0n · Answer

*cos(pi/3)

p0sitr0n · Answer

2*1/2*$$\sqrt{3}/2 $$ = 3^1/2/2

anonymous · Answer

sin(2π/3) = sin(π/3)

anonymous · Answer

*cough* unit circle *cough*

p0sitr0n · Answer

anonymous · Answer

I was thinking Sin(2pi/3) would be in the II quadrant.

anonymous · Answer

I see it on the unit circle, but my teacher told me, Sine can't be in the quadrant because it has a range of +/- pi/2

p0sitr0n · Answer

range of sine is from -1 to 1. its domain is R

anonymous · Answer

Oh, so the range of sin^-1 is +/- pi/2 then right?

p0sitr0n · Answer

its an inverse function. dom f(x) = range f^-1(x)

p0sitr0n · Answer

range of arcsin (sin^-1) is R. its like the sin but tilted 90 degrees. domain is [-1,1]

anonymous · Answer

You'll only have to worry about the domain of arctangent here, but it won't be a problem.

anonymous · Answer

Okay, I got that part down, so how should I figure out the rest of the problem? Should my answer be in radians or...

anonymous · Answer

$$\sin(\frac{2\pi}{3})=\frac{\sqrt{3}}{2}$$
$$\tan^{-1}(\frac{\sqrt{3}}{2})$$ is a calculator exercise

anonymous · Answer

But the thing is, the teacher doesn't want us to use a calculator. It's more of a memorize the unit circle excercise.