Question

Which of the expressions (on the photo document I inserted) together represent all solutions to the following equation?

8cos(12x)+4=-4

*The answer should be in degrees.*

> I would like for someone to explain the process to find the solutions for this.

Answer 1

Answer:

x =15 + 30n

Step-by-step explanation:

8cos(12x)+4=-4

Subtract 4 from each side

8cos(12x)+4-4=-4-4

8cos(12x)=-8

Divide by 8

8/8cos(12x)=-8/8

cos(12x) = -1

Take the arccos on each side

arccos(cos(12x)) = arccos(-1)

12x = 180 degrees  

But we can go around in a circle of 360 and get the same result

12 x = 180+360n  where n is an integer

Divide each side by 12

x = 180/12 +360n/12

x =15 + 30n