# Thread: Solving a Trigonometric Equation

1. ## Solving a Trigonometric Equation

Solve for x:
cos (x) = 3x/(2pi)

The asnwer is pi /3 but how is it solved algebraically???

2. I don't think this can be solved algebraically...

3. ok. Then how can I prove that pi/3 is the answer?

4. LHS = cos(pi/3) = 1/2

RHS = 3(pi/3)/(2pi) = pi/(2pi) = 1/2 = LHS.

So x = pi/3 is a solution.

5. Yes x = pi/3 is a solution.
But how is x = pi/3 derived in the first place???

Originally Posted by Prove It
LHS = cos(pi/3) = 1/2

RHS = 3(pi/3)/(2pi) = pi/(2pi) = 1/2 = LHS.

So x = pi/3 is a solution.

6. Originally Posted by bakchormee
Yes x = pi/3 is a solution.
But how is x = pi/3 derived in the first place???
Probably from examining the point of intersection of the graphs of y = cos(x) and y = 3x/(2pi), or using numerical methods.

7. What do you mean by numerical methods?

Yes by graphing it, the point of intersection if x = pi/3.
But i need to know it is derived...?

8. Originally Posted by bakchormee
What do you mean by numerical methods?

Yes by graphing it, the point of intersection if x = pi/3.
But i need to know it is derived...?
Numerical methods are iterative methods, such as the Bisection Method or Newton's Method. Google them.

Like I said, this point of intersection can NOT be solved algebraically, because you have a trigonometric function on one side and a polynomial function on the other. There is no way to combine them...

9. Thanks for that.
I having problems deriving x to show the prove though.....