# Solving a Trigonometric Equation

• May 10th 2011, 09:50 PM
bakchormee
Solving a Trigonometric Equation
Solve for x:
cos (x) = 3x/(2pi)

The asnwer is pi /3 but how is it solved algebraically???
• May 10th 2011, 09:56 PM
Prove It
I don't think this can be solved algebraically...
• May 10th 2011, 09:58 PM
bakchormee
ok. Then how can I prove that pi/3 is the answer?
• May 10th 2011, 10:04 PM
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.
• May 10th 2011, 10:17 PM
bakchormee
Yes x = pi/3 is a solution.
But how is x = pi/3 derived in the first place???

Quote:

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.

• May 10th 2011, 10:28 PM
Prove It
Quote:

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.
• May 10th 2011, 10:30 PM
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...?
• May 10th 2011, 10:32 PM
Prove It
Quote:

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...
• May 10th 2011, 10:51 PM
bakchormee
Thanks for that.
I having problems deriving x to show the prove though.....