Question

Find all the values of x in the interval [0,2π) that satisfy the equation:

12cos(2x+2π)=21
This equation is ready to be solved for x in the specified interval [0,2π).

Answer 1

To solve the equation 12cos(2x+2π)=21 in the interval [0,2π), divide both sides by 12, apply the inverse cosine function, subtract 2π, and divide by 2 to find x.

Step-by-step explanation:

To solve the equation 12cos(2x+2π)=21 in the interval [0,2π), we need to isolate the cosine term and then solve for x.

Step 1: Divide both sides of the equation by 12: cos(2x+2π) = 21/12 = 7/4.

Step 2: Apply the inverse cosine function to both sides to get rid of the cosine: 2x+2π = arccos(7/4).

Step 3: Subtract 2π from both sides: 2x = arccos(7/4) - 2π.

Step 4: Divide both sides by 2: x = (1/2)(arccos(7/4) - 2π).

The values of x that satisfy the equation in the interval [0,2π) can be found by plugging in the values of arccos(7/4) and 2π into the expression for x.