I don't understand them at all.

The problem is to evaluate tan(22.5) using exact values.

How should I do this?

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- Jul 21st 2009, 12:36 PMhellojellojwHalf angle or double angle Identities
I don't understand them at all.

The problem is to evaluate tan(22.5) using exact values.

How should I do this? - Jul 21st 2009, 12:47 PMKrizalid
$\displaystyle \tan \frac{x}{2}=\frac{\sin \frac{x}{2}}{\cos \frac{x}{2}}=\frac{\sqrt{\frac{1-\cos x}{2}}}{\sqrt{\frac{1+\cos x}{2}}}=\sqrt{\frac{1-\cos x}{1+\cos x}}.$

Actually is $\displaystyle \sin \frac{x}{2}=\pm \sqrt{\frac{1-\cos x}{2}},$ but the angle is positive, hence our answer is positive, and that's preserves the positive sign. - Jul 21st 2009, 01:10 PMhellojellojw
- Jul 21st 2009, 01:52 PMpickslides
Krizalid is suggesting $\displaystyle x = \frac{\pi}{4}$

- Jul 21st 2009, 05:20 PMhellojellojw
Well, that was easier than I expected. Thanks.