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# How do you find the general solution for cos of 3x- pi over 3 equals 0.5?

Updated: 12/11/2022

Wiki User

13y ago

cos (3pi x/3) = 0.5

The number of answers depends on the range of angles. I will solve this question using the range 0<x<2 pi. Draw a unit circle, you will see that the quadrants where cosine gives a positive value are the first and the fourth quadrants.

The Angles whose cosines give + 0.5 are: pi / 3 and 5pi / 3. (Note that 7 pi/3 and 11 pi/3 are also possible solutions but they lie out of the range 0<x<2pi.)

3pi x/3 = pi/3 OR 3pi x/3 = 5pi/3

Here you can solve the equations to give x = 1/3; 5/3

Wiki User

13y ago

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Q: How do you find the general solution for cos of 3x- pi over 3 equals 0.5?
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