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

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- March 21st 2010, 05:15 PMChinnie15sin(cosx)=0
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 - March 21st 2010, 05:39 PMskeeter
this equation is not true for all x (not an identity) ... it is a conditional equation, so there is nothing to "prove".

since , then has to be 0 or an integer multiple of .

since , none of the multiples of will work, therefore can only equal 0.

I leave you to determine those values of x that make - March 21st 2010, 05:45 PMChinnie15
Oh ok, thanks! So if cos90=0.. that would get me my answer?

- March 21st 2010, 05:48 PMskeeter
- March 21st 2010, 05:53 PMChinnie15
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