Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)? 18 cos(x) - 9 = 0

Solution:

Given, the equation is 18 cos(x) - 9 = 0

We have to all values of x in the interval [0, 2π]

Now, 18 cos(x) = 9

cos(x) = 9/18

cos(x) = 1/2

We can use the unit circle to find which angles satisfy the equation.

Points on the unit circle are (cos, sin)

So, any point on the unit circle that has an x value of 1/2 is a solution.

We know,

cos(π/3) = 1/2

cos(5π/3) = 1/2

Therefore, the values of x are π/3, 5π/3.

Find all values of x in the interval [0, 2π] that satisfy the equation. (Enter your answers as a comma-separated list.)? 18 cos(x) - 9 = 0

Summary:

All the values of x in the interval [0, 2π] that satisfy the equation 18 cos(x) - 9 = 0 are π/3, 5π/3.