sin(cosx)=0

**Chinnie15** · March 21st 2010, 05:15 PM

I need to prove sin(cosx)=0, but I'm looking through all of my identities and none of them seem to fit? Any help on this would be great!

Thank you!
Brittney

**skeeter** · March 21st 2010, 05:39 PM

Originally Posted by Chinnie15

I need to prove sin(cosx)=0, but I'm looking through all of my identities and none of them seem to fit? Any help on this would be great!

Thank you!
Brittney

this equation is not true for all x (not an identity) ... it is a conditional equation, so there is nothing to "prove".

since $\sin(something) = 0$ , then $something$ has to be 0 or an integer multiple of $\pi$ .

since $-1 \le \cos{x} \le 1$ , none of the multiples of $\pi$ will work, therefore $\cos{x}$ can only equal 0.

I leave you to determine those values of x that make $\cos{x} = 0$

**Chinnie15** · March 21st 2010, 05:45 PM

Oh ok, thanks! So if cos90=0.. that would get me my answer?

**skeeter** · March 21st 2010, 05:48 PM

Originally Posted by Chinnie15

Oh ok, thanks! So if cos90=0.. that would get me my answer?

that would be one possible solution.

**Chinnie15** · March 21st 2010, 05:53 PM

Ok, I think I get it now. So cos of 270 is also equal to zero. And then all coterminal angles of 90 and 270?

Edit: Here is my solution for my hw- Sin(cos x)=0 when x is 90±360 or 270±360. Sin(cos x)--> Sin(0) --> 0

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