Trig Equation

Date: 6/22/96 at 9:54:16
From: Igor Srdanovic
Subject: Trig. Equation

Hi!
 
I have a math problem. It's an equation. Hope you can solve it.
 
(cos(x))^2+(sin(x))^2=(15*(cos(x))^2)/18)-(1/2)
 
x=?

Date: 6/22/96 at 11:8:49
From: Doctor Anthony
Subject: Re: Trig. Equation

As you have written the equation, the left hand side will equal 1. 
The equation then can be written:

(15/18)cos^2(x) - 1/2 = 1

        (5/6)cos^2(x) = 3/2

             cos^2(x) = 18/10

             cos^2(x) = 1.8

             cos(x) = sqrt(1.8) = 1.34164

There can be no real solution to this equation since 
-1 < or = cos(x) < or = 1 for real x. I have some doubts about the 
equation you have written down, particularly as the left hand side 
immediately simplifies to 1.  Perhaps you can check it and post a 
correction if necessary.

-Doctor Anthony,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/