Question

Solve for x on the interval 0≤x<2pi cos(3x)=1/2

Answer 1

We will see that the solution in the given interval is: x = 0.349 radians.

How to solve equations with the variable in the argument of a cosine?

We want to solve:

cos(3*x) = 1/2

Here we must use the inverse cosine function, Acos(x). Remember that:

cos(Acos(x)) = Acos(cos(x)) = x.

If we apply that in both sides, we get:

Acos( cos(3x) ) = Acos(1/2)

3*x = Acos(1/2)

x = Acos(1/2)/3 = 0.349

So x is equal to 0.349 radians, which belongs to the given interval.

If you want to learn more about trigonometry, you can read:

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