# Thread: trigo problem no. 24 [general solution]

1. ## trigo problem no. 24 [general solution]

p215 q10
thanks

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

3. 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.

4. Originally Posted by afeasfaerw23231233
i didn't treat cos 2x as cos ^2 x
I looked at the line wrong. My apologies.

-Dan