# Sine and Cosine

• Feb 10th 2010, 02:55 PM
nuckers
Sine and Cosine
Not sure what this question is asking me, when their is no numbers to calculate, can someone please explain this to me

If Cos(x)=m then what is the value of Cos (180-x)?

Thanks
• Feb 10th 2010, 03:03 PM
danielomalmsteen
$\displaystyle \cos(a-b) = \cos a \cos b + \sin a \sin b$
• Feb 10th 2010, 03:12 PM
icemanfan
It's a trigonometric identity.

cos(180 - x) is always the opposite of cos(x).

You could come to that conclusion several ways, but the easiest method is to look at a typical angle Q on a graph and compare it with its supplement (which is defined as 180 - Q), and then you will see why the conclusion is true.
• Feb 10th 2010, 03:25 PM
nuckers
Quote:

Originally Posted by icemanfan
It's a trigonometric identity.

cos(180 - x) is always the opposite of cos(x).

You could come to that conclusion several ways, but the easiest method is to look at a typical angle Q on a graph and compare it with its supplement (which is defined as 180 - Q), and then you will see why the conclusion is true.

so the answer that i would be looking for then is -cos(180-x), or am i way out to lunch on this one
• Feb 10th 2010, 03:31 PM
icemanfan
Quote:

Originally Posted by nuckers
so the answer that i would be looking for then is -cos(180-x), or am i way out to lunch on this one

Well, if cos(x) = m and cos(180 - x) is the opposite of cos(x), then what does cos(180 - x) equal in terms of m?
• Feb 10th 2010, 03:31 PM
skeeter
Quote:

Originally Posted by nuckers
so the answer that i would be looking for then is -cos(180-x), or am i way out to lunch on this one

if $\displaystyle \cos{x} = m$ , then $\displaystyle \cos(180-x) = -m$

... that's all.
• Feb 10th 2010, 03:33 PM
nuckers
Quote:

Originally Posted by icemanfan
Well, if cos(x) = m and cos(180 - x) is the opposite of cos(x), then what does cos(180 - x) equal in terms of m?

Ok, i understand now, thanks so much for the help