trigo problem no. 24 [general solution]

**afeasfaerw23231233** · March 25th 2008, 08:38 AM

p215 q10
thanks

**afeasfaerw23231233** · March 25th 2008, 09:50 PM

i didn't treat cos 2x as cos ^2 x

**mr fantastic** · March 26th 2008, 02:51 AM

Originally Posted by afeasfaerw23231233

i didn't treat cos 2x as cos ^2 x

1. Your answer of $\frac{2n\pi}{3} \pm \frac{\pi}{6}$ is correct, the book's answer of $2n\pi + \frac{\pi}{6}$ misses solutions $\left( \text{such as} \, \frac{5\pi}{6} \, \text{and} \, \frac{\pi}{2}\right)$ and so is not completely correct .....

2. $\cos^{-1} \left( \frac{-1 + \sqrt{5}}{4} \right) = \frac{2 \pi}{5}$ and $\cos^{-1} \left( \frac{-1 - \sqrt{5}}{4} \right) = \frac{4 \pi}{5}$ are correct exact values. Your corresponding answers are only decimal approximations to these exact answers. But it's a bit tough to expect someone to know these exact values!!!!

It's possible to prove that these are the exact values but it's a bit complicated.

**topsquark** · March 26th 2008, 03:53 AM

Originally Posted by afeasfaerw23231233

i didn't treat cos 2x as cos ^2 x

I looked at the line wrong. My apologies.

-Dan

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