# Thread: Vaules of Cos and Sin and stuff

1. ## Vaules of Cos and Sin and stuff

Explain why the value of [cosX, sinX]*[cos(90+X), sin(90+X)] is independent of X.

X=theta

what does independent of X even mean?

2. Originally Posted by stones44
Explain why the value of [cosX, sinX]*[cos(90+X), sin(90+X)] is independent of X.

X=theta
i suppose you mean the dot product here? just take the dot product and use the addition formula for the functions in the second pair of brackets and simplify

what does independent of X even mean?
it means that it does not matter what X is, the value will be the same no matter what X we choose

3. ehhh im confused

4. Originally Posted by stones44
ehhh im confused
$\displaystyle \cos (A + B) = \cos A \cos B - \sin A \sin B$

$\displaystyle \sin (A + B) = \sin A \cos B + \sin B \cos A$

now apply those identities, take the dot product and simplify. you will see that it does not matter what x is

5. Originally Posted by stones44
Explain why the value of [cosX, sinX]*[cos(90+X), sin(90+X)] is independent of X.

X=theta

what does independent of X even mean?
Assuming dot product: if you simplify this properly you will have $\displaystyle -\sin(x)\cos(x)+\cos(x)\sin(x)$, which is?

RonL