Without using a calculator, find the value for f(pi/3) if the function f(x)=sin^-1(Cos x). Give exact answers. The dependent variable is in radians.

Question

anonymous · Answer

$$f(\frac{ \pi }{ 3})    $$ if the function $$f(x)=\sin^{-1} (\cos x)$$

anonymous · Answer

so our equation would update to $$f (\frac{ \pi }{ 3})=\sin^{-1} (\cos \frac{ \pi }{ 3 })$$

I think.

zehanz · Answer

If you don't know the value of cos(pi/3) by heart (shame on you!), you can find it with the unit circle...pi/3 equals 60 degrees, so if you mark 60 deg on the unit circle, you will get the well-known(?) 30-60-90 triangle with the sides we all know and love:

½, 1 and ½√3. One of these is cos(pi/3)...

anonymous · Answer

Okay, so then we have three possible equations, what do we do then?

zehanz · Answer

Look at this image and remember where you can find cos 60 degrees in it:

anonymous · Answer

I understand that the cos(pi/3)=60 degrees, but I'm not even sure I understand what I'm trying to find... I'm sorry I'm really not trying to be thick.

zehanz · Answer

You need to find $$\sin^{-1}(\cos(\frac{ \pi }{ 3 }))$$so I would first try to figure out what cos(pi/3) is. (work from the inside to the outside, so to speak...)

Now cos(pi/3) = cos(60 degrees) = ½. You know that, I think.

Now you are left with :$$\sin^{-1}(\frac{ 1 }{ 2 })$$Doesn't that sound familiar? You are looking for an angle of which the sine is ½. That is also a well known angle...