Trigonometric equation...

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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
 
americo74 said:
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...

cos(y)=32\displaystyle \cos(y) = \frac{\sqrt{3}}{2} has solutions y=π6+2kπ\displaystyle y = \frac{\pi}{6} + 2k\pi and 11π6+2kπ\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.
 
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