Solving an Equation with Cosine

[salman213]

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

x is known
r is known

I can't 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!

Homework Equations

The Attempt at a Solution

 

[quantumdude]

Here's your problem right here:

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

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

 

[salman213]

yea sorry that's what i meant

but it still doesn't work out..

 

[quantumdude]

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

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

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

 

[salman213]

Who is Egad?EDITED!

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

Thanks anyways!

 

[quantumdude]

Who is Egad?

"egad" is an exclamation like "crikey" or "blimey".