# Cos sin problem?

• Feb 4th 2009, 08:16 PM
view360
Cos sin problem?
Hello. I have a test tomorrow and I'm not sure in one area.

$<\cos \theta, \sin \theta> \cdot <\cos (180+ \theta), \sin(180+ \theta)>$

Explain why the value does not depend on the value of $\theta$.

Could someone please talk me through this step by step? thanks.
• Feb 4th 2009, 08:19 PM
Jhevon
Quote:

Originally Posted by view360
Hello. I have a test tomorrow and I'm not sure in one area.

$<\cos \theta, \sin \theta> \cdot <\cos (180+ \theta), \sin(180+ \theta)>$

Explain why the value does not depend on the value of $\theta$.

Could someone please talk me through this step by step? thanks.

here's something you probably never thought of, take the dot product. what do you get?
• Feb 4th 2009, 08:23 PM
view360
Quote:

Originally Posted by Jhevon
here's something you probably never thought of, take the dot product. what do you get?

$<\cos \theta \cos(180+\theta), \sin \theta \sin(180+ \theta)>$
• Feb 4th 2009, 08:28 PM
Jhevon
Quote:

Originally Posted by view360
cos $theta$cos(180+ $theta$), sin $theta$sin(180+ $theta$)

that's not the dot product

$\left< a,b \right> \cdot \left< c,d \right> = ac + bd$
• Feb 4th 2009, 08:30 PM
view360
$\cos \theta \cos(180+ \theta) + \sin \theta \sin (180+ \theta)$?

btw is this really calc? I'm only a freshman, isn't calc a much more advanced class?
• Feb 4th 2009, 08:34 PM
Jhevon
Quote:

Originally Posted by view360
cos $theta$cos(180+ $theta$) + sin $theta$sin)180+ $theta$)?

yes, now recall that $\cos (A - B) = \cos A \cos B + \sin A \sin B$

Quote:

btw is this really calc? I'm only a freshman, isn't calc a much more advanced class?
yeah, you're right. i was tutoring calc 3 today and we were working with dot products, so my mind automatically filed this under calculus :p i'll have it changed.
• Feb 4th 2009, 08:41 PM
view360
Quote:

Originally Posted by Jhevon
yes, now recall that $\cos (A - B) = \cos A \cos B + \sin A \sin B$

yeah, you're right. i was tutoring calc 3 today and we were working with dot products, so my mind automatically filed this under calculus :p i'll have it changed.

Sorry if I sound stupid lol, but i'm not making any connections between the two?
• Feb 4th 2009, 08:44 PM
Jhevon
Quote:

Originally Posted by view360
Sorry if I sound stupid lol, but i'm not making any connections between the two?

replace A with $\theta$ and replace B with $180 + \theta$

do you see it now?
• Feb 4th 2009, 08:51 PM
view360
Quote:

Originally Posted by Jhevon
replace A with $\theta$ and replace B with $180 + \theta$

do you see it now?

Oh okay, so it equals cos(A-B), which if you replace it, equals cos(theta-180+theta). So it ends up just equaling cos180, the theta doesn't change that. But why is A = $\theta$ and B $180 + \theta$?