Use an identity to write each expression as a trig function value or as a single number.

1-2sin^2(22 1/2 degrees)

and

1/4 - 1/2 sin^2 (47.1 degrees)

Thanks for reading!

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- Oct 29th 2009, 08:13 PMThatoneguy12345Double Angle Identities
Use an identity to write each expression as a trig function value or as a single number.

1-2sin^2(22 1/2 degrees)

and

1/4 - 1/2 sin^2 (47.1 degrees)

Thanks for reading! - Oct 29th 2009, 11:49 PMGrandad
Hello Thatoneguy12345These both use the identity $\displaystyle \cos2\theta =1-2\sin^2\theta$

1) $\displaystyle 1-2\sin^222\tfrac12^o=\cos 45^o=\frac{1}{\sqrt2}$

2) $\displaystyle \tfrac14-\tfrac12\sin^247.1^o=\tfrac14(1-2\sin^247.1^o)=\tfrac14\cos 94.2^o$, and you can't simplify this any further.

Grandad - Oct 29th 2009, 11:51 PMThatoneguy12345
wait for the first one, how did you get cos45?

I begin with 1 - 2 sin ^ 2 (22 1/2) and I end up multiplying the 22 with 1/2 and getting 11. So I end up with 1-2sin^2 11. Is that the correct step?

NVM I get it! Thanks a lot