1. ## 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.

2. 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?

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

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

4. Originally Posted by view360
cos $theta$cos(180+ $theta$), sin $theta$sin(180+ $theta$)
that's not the dot product

$\left< a,b \right> \cdot \left< c,d \right> = ac + bd$

5. $\cos \theta \cos(180+ \theta) + \sin \theta \sin (180+ \theta)$?

btw is this really calc? I'm only a freshman, isn't calc a much more advanced class?

6. Originally Posted by view360
cos $theta$cos(180+ $theta$) + sin $theta$sin)180+ $theta$)?
yes, now recall that $\cos (A - B) = \cos A \cos B + \sin A \sin B$

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 i'll have it changed.

7. 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 i'll have it changed.

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

8. 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?

9. 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 $180 + \theta$?