Math Forums @ Math Goodies - Equations with Trig functions

testing header

Math Goodies is a free math help portal for students, teachers, and parents.

| More

Interactive Math Goodies Software

Math Forums @ Math Goodies

Username:	Password:
Save Password
Forgot your Password?

All Forums

Homework Help Forums

Algebra

Equations with Trig functions

New Topic

Reply to Topic

Printer Friendly

Author

Topic

mathphobic
Average Member

USA
8 Posts

Posted - 10/23/2007 : 19:20:24

Can this be solved algebraically?

sqrt(3) * cos x + sin x = 1

I was asked to find the answers exactly, but I'm not sure how to do that with that equation.

skeeter
Advanced Member

USA
5634 Posts

Posted - 10/23/2007 : 20:00:48

(3)*cosx + sinx = 1

(3)*cosx = 1 - sinx

square both sides ...

3cos

x = 1 - 2sinx + sin

x

use a well known identity ...

3(1 - sin

x) = 1 - 2sinx + sin

x

3 - 3sin

x = 1 - 2sinx + sin

x

0 = 4sin

x - 2sinx - 2

0 = 2sin

x - sinx - 1

0 = (2sinx + 1)(sinx - 1)

sinx = -1/2 ... x = 7

/6, x = 11

/6

sinx = 1 ... x =

/2

use the original equation to check for possible extraneous solutions.

mathphobic
Average Member

USA
8 Posts

Posted - 10/23/2007 : 21:29:14

Thank you skeeter. It never occurred to me to square both sides.

Subhotosh Khan
Advanced Member

USA
9115 Posts

Posted - 10/24/2007 : 07:44:15

quote:
Originally posted by mathphobic

Can this be solved algebraically?

sqrt(3) * cos x + sin x = 1

I was asked to find the answers exactly, but I'm not sure how to do that with that equation.

If you have an expression like

A * cos