# Homework Help: Solving an Equation with Cosine

1. Feb 18, 2009

### salman213

1.x = rcos(a)cos(a)

x is known
r is known

I cant seem to get this!

x = -2
r = 7

therefore

-2/7 = cos(a)*cos(a)

so..

-2/7 = cos^2(a)

i know cos^2(a) = 1 + cos2a / 2

-2/7 = 1 + cos2a / 2

so
-4/7 -1 = cos2a

I cannot take cos inverse of this value since it is "greater" than 1 (-1.57)

the book says the angle is 106.6 degrees!!!

HELP!

2. Relevant equations

3. The attempt at a solution

2. Feb 18, 2009

### Tom Mattson

Staff Emeritus

Nope, it's $\cos^2(a)=(1+\cos(2a))/2$. Both terms are divided by 2.

3. Feb 18, 2009

### salman213

yea sorry thats what i meant

but it still doesnt work out..

4. Feb 18, 2009

### Tom Mattson

Staff Emeritus
Egad, you have an even more serious problem that I missed.

You can't square cos(a) and get a negative number. This equation has no solution in the real numbers.

5. Feb 18, 2009

### salman213

EDITED!!!

NEVERMIND I figured it out, i was interpreting the solution incorrectly...

Thanks anyways!!

6. Feb 19, 2009

### Tom Mattson

Staff Emeritus
:rofl: "egad" is an exclamation like "crikey" or "blimey".