2cos 4theta + 1 = 0

i know how to find the degrees (the last step of the problem), but i don't know how to start the problem. Could someone please show me the steps?

I assume you mean cos (4 theta) and not
(cos theta)^4

cos (4 theta) = -1/2
The angles with a cosine equal to -1/2 are: 120 and 240 degrees, and also 480 and 600 degrees, and 840 and 960 degrees etc (Just adding 360 degrees to previous answers). . Since that is 4 theta, divide any of those numbers by 4 for theta values that are solutions.
THETA = 30, 60, 120, 150, 210, 240...degrees

To solve the equation 2cos(4θ) + 1 = 0, you want to isolate the cosine term and then solve for theta. Here are the steps to solve this equation:

1. Start by subtracting 1 from both sides of the equation: 2cos(4θ) = -1.

2. Divide both sides of the equation by 2: cos(4θ) = -1/2.

3. Now, to find the values of θ that satisfy this equation, you need to find the angles at which the cosine function equals -1/2.

4. The angles with cosine equal to -1/2 are 120 and 240 degrees, and so on. This is because the cosine function has a repeating pattern every 360 degrees.

5. Since the given equation is for cos(4θ), you need to divide those angles by 4 to find the values of θ that satisfy the equation.

6. Divide 120 degrees by 4 and you get 30 degrees. Divide 240 degrees by 4 and you get 60 degrees.

7. Therefore, the possible values of θ that satisfy the equation are 30 degrees and 60 degrees.

So, the solution to the equation 2cos(4θ) + 1 = 0 is θ = 30 degrees and θ = 60 degrees.