√3 + 5cos⦸ = 3 cos⦸

Can someone please explain for me how to express the answer in radian measure?

Thanks

√3 + 5cosθ = 3cosθ

2cosθ = -√3
cosθ = -√3/2

θ = 5π/6 or 7π/6

thank you steve!!

To express the answer in radian measure, you need to solve the equation √3 + 5cos⦸ = 3cos⦸, where ⦸ is an angle.

First, let's simplify the equation by moving all terms to one side:
√3 + 5cos⦸ - 3cos⦸ = 0

Combine the cosine terms:
√3 + (5 - 3)cos⦸ = 0
√3 + 2cos⦸ = 0

To solve this equation, we need to isolate the cosine term. We can do this by moving the constant (√3) to the other side:
2cos⦸ = -√3

Next, divide both sides of the equation by 2 to solve for cos⦸:
cos⦸ = -√3/2

Now, to express the solution in radian measure, we need to find the corresponding angle(s) whose cosine is equal to -√3/2.

Recall that the cosine function is positive in the first and fourth quadrants.

Using the unit circle or a trigonometric table, we can find that the reference angle with a cosine of -√3/2 is π/6 radians.

Since the cosine value is negative, the angle must lie in the second or third quadrant. By considering the symmetry of the cosine function, we can conclude that the angle is π - π/6 in the second quadrant, or π + π/6 in the third quadrant.

Therefore, the angles that satisfy the equation are:
⦸ = π - π/6
⦸ = π + π/6

So the answer expressed in radian measure is ⦸ = π - π/6 or ⦸ = π + π/6.