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 one year 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.
 one year 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.

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natnatwebb
 one year ago
Best ResponseYou've already chosen the best response.0\[f(\frac{ \pi }{ 3}) \] if the function \[f(x)=\sin^{1} (\cos x)\]

natnatwebb
 one year ago
Best ResponseYou've already chosen the best response.0so our equation would update to \[f (\frac{ \pi }{ 3})=\sin^{1} (\cos \frac{ \pi }{ 3 })\] I think.

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1If 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 wellknown(?) 306090 triangle with the sides we all know and love: ½, 1 and ½√3. One of these is cos(pi/3)...

natnatwebb
 one year ago
Best ResponseYou've already chosen the best response.0Okay, so then we have three possible equations, what do we do then?

ZeHanz
 one year ago
Best ResponseYou've already chosen the best response.1Look at this image and remember where you can find cos 60 degrees in it:

natnatwebb
 one year ago
Best ResponseYou've already chosen the best response.0I 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
 one year ago
Best ResponseYou've already chosen the best response.1You 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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