How do you solve this trig equation?

Question

I feel so rusty with trig now - your help is truly appreciated.

Use a calculator, if necessary; find all solutions for the trig equation:

2cos3x = 0.45

Answer 1

2cos3x = 0.45

Cos3x = 0.45/2

          = 0.255(Cos x is positive in the first and fourth quadrant, therefore there are 2 values of x)

3x =cos-1 0.225

3x = 76.997

X = 76.997/3

   = 25.666

Therefore X= 25.7, (360- 25.666)

        = 25.7,334.3 (from 0 to 360)

Answer 2

2cos3x    =   0,45

So cos3x  =  0,225

Therefore 3x = 76,991 degrees

But sin x = sin(x + - n360)

So 3x  =  77+ - n( 360)

x = 25,67 + - n( 120) degrees     Where n is a interger

Answer 3

2cos3x = 0.45

==> cos(3x) = 0.225

==> cosˉ¹(0.225) = 3x

==> x = (1/3)cosˉ¹(0.225)

==> x ≈ 25.67

Make sense?

Hope this helps.

***** Ok.....with these you isolate the trig function, in this case the "cos(3x)", then when you get to this part..."cosˉ¹(0.225) = 3x"....you have to solve this part with the inverse trig function using a calculator.

Better?

>>>> No need to feel silly. You didn't know and you asked the question. Nothing wrong with that at all. Glad to help, and no need to promise me points. Maybe someone else will post a better response which would be more deserving of the points. I'm not here to accrue big points....just help folks. If I get points for it......great, if not, that's ok too. I don't compete....I just have fun!     :)