If 4x = 60° + 360°k, then what does x equal? Explain. State the values of x if 0° < x < 360°.

Answer 1

Divide both sides of the equation 4x=60 + 360k by 4 to get x = 15+90k.

This could be the result (for example) of solving the equation cos(4x) = 1/2.

4x = cos^-1(1/2)

4x = 60 + 360k , k any integer. There is another solution too: 4x = 300 + 360k, k any integer.

To finish solving for x, do that division by 4.

x = 15 + 90k or x = 75 + 90k, k any integer. This is typically how you would represent the infinitely many angles that have a cosine of 1/2. Some texts use +360n, n any integer.

For the stipulated equation, to find the values of x between 0 and 360

let k = 0, 1, 2,3

x = 15 +0(90), 15+1(90), 15+2(90), 15+3(90)

x= 15, 105, 195, 285

Here is an example where f(x) = cos(4x)

desmos.com/calculator/kacvdvrwtv