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natnatwebb
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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
 one year ago
natnatwebb Group Title
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
 one year ago

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

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

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

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

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

natnatwebb Group TitleBest ResponseYou've already chosen the best response.0
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.
 one year ago

ZeHanz Group TitleBest ResponseYou've already chosen the best response.1
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...
 one year ago
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