Solve the equation on the interval?

Question

Trigonometry Equation

 

6 cos ² 0 = 3

 

Please I need step by step instruction on how the answers where found.

 

Thank You for being so Helpfull,

Bella

Answer 1

6 cos² x = 3

Is that your question?

If so,



Divide both sides by 6:

(6 cos² x)/6 = 3/6

cos² x = 1/2


Take the square root of both sides:
cos x = +/- sqrt(1/2)

cos x = +/- (√2)/2

Cos x = +/- Sqrt(2)/2 at every multiple of pi/4

cos pi/4 = Sqrt(2)/2

cos 3pi/4 = - sqrt(2)/2

cos 5pi/4 = - sqrt(2)/2

cos 7pi/4 = sqrt(2)/2

...

 

So x = (pi)(2n+1)/4 for n = 0,1,2,3...

 

It depends on if they gave you an interval to use for the solution set.

 

 

For example, they could have said x or "theta" such that 0<= x <= 2pi.

 

If so, the answers would be x = {pi/4, 3pi/4, 5pi/4, 7pi/4}