## natnatwebb 2 years ago 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.

1. natnatwebb

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

2. natnatwebb

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

3. ZeHanz

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)...

4. natnatwebb

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

5. ZeHanz

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

6. natnatwebb

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.

7. ZeHanz

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...
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