Trigonometric equation...

[Guest]

Find all values of x when,
2 cos (2x-pi/3) = root 3

My solutions are: x = pi/14 and 5pi/4...textbook says pi/12,pi/4,13pi/2,5pi/4

 

[tkhunny]

Find all values of x when,
2 cos (2x-pi/3) = root 3

My solutions are: x = pi/14 and 5pi/4...textbook says pi/12,pi/4,13pi/2,5pi/4

Let's see...

\(\displaystyle \cos(y) = \frac{\sqrt{3}}{2}\) has solutions \(\displaystyle y = \frac{\pi}{6} + 2k\pi\) and \(\displaystyle \frac{11\pi}{6} + 2k\pi\) where k is Integer.

\(\displaystyle \L\;2x - \frac{\pi}{3} = \frac{\pi}{6} + 2k\pi\)

\(\displaystyle \L\;x - \frac{\pi}{6} = \frac{\pi}{12} + k\pi\)

\(\displaystyle \L\;x = \frac{\p}{4} + k\pi\)

You do the other one.