Solve the trigonometric equation in the interval [0, 2𝜋). Give the exact value, if possible; otherwise, round your answer to two decimal places. 7 cos(2𝜃) = 6

Answer 1

From the equation y = 7cos(2θ), we know that it starts at y=7 and moves down from there. At least one solution should be between θ = 0 and θ = 2π.

Let's rearrange the equation:

cos(2θ) = 6/7

Substitute x = 2θ. What value of x is cos(x) = 6/7?

To find this, use the arccos equation and plug in the value you're looking for the angle of.

arccos(6/7) = x = 31°

Divide this value by 2 to get back to our original θ and we get θ = 15.5° or 0.27 radians.