# solving cos.

• Nov 25th 2007, 10:09 AM
overduex
solving cos.
Hi! If anyone could please explain this, I would really appreciate it.

I'm doing my math hw and trying to use the calculator as little as possible.
one of the problems is verifying the x-value.
the step I am currently on looks like this:

4cos^2 (45 degrees) -2 =0

my question is. Could anyone possibly explain how to find 4cos^2 (45) by hand (not using a calculator)????? When I put it into the calculator it says te answer is 2. But I want to know how to find that by hand...is it possible???
do you square the 45 first and then multiply by 4 and find the cos of that?????

thanks again!!!
and please let me know if my question does not make sense :/
• Nov 25th 2007, 10:17 AM
topsquark
Quote:

Originally Posted by overduex
Hi! If anyone could please explain this, I would really appreciate it.

I'm doing my math hw and trying to use the calculator as little as possible.
one of the problems is verifying the x-value.
the step I am currently on looks like this:

4cos^2 (45 degrees) -2 =0

my question is. Could anyone possibly explain how to find 4cos^2 (45) by hand (not using a calculator)????? When I put it into the calculator it says te answer is 2. But I want to know how to find that by hand...is it possible???
do you square the 45 first and then multiply by 4 and find the cos of that?????

thanks again!!!
and please let me know if my question does not make sense :/

$4cos^2(45^o) = 4 ( cos(45^o) )^2 = 4 \left ( \frac{\sqrt{2}}{2} \right ) ^2 = 4 \frac{2}{4} = 2$

-Dan