# Cos 2x=0.32

### Solution:

First let’s apply the reverse cosine function to both sides of the equation:

**cos ^{-1}(cos(2x)) = cos^{-1} (0.32) = cos^{-1} (**

**)**

Now if you take the inverse cosine the cosine of 2x, you get 2x…so:

**2x = cos ^{-1} ()**

**2x **** 71.34°**

** x**** **** 35.67° (which is approximately the same as 0.622 radians)**

This looks like it might be the final answer, but actually it’s only one of the many correct answers. One way to see this is by graphing y=cos(2x) and seeing where it intersects the line y=0.32. If you do this, you will see that the intersections occur at multiple points:

As you can see, the intersections occur at x 0.622 radians, 2.519 radians, 3.764 radians, 5.660 radians, etc. The general form of the solution set is as follows:

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