Q) Express 3 sin x + 4 cos x in the form R cos (x-a) a is alpha

any idea i think we must change the sinx into cos x (Worried)

Printable View

- Apr 10th 2008, 10:33 AMmanutd4lifeR formulae (double angle formulae) URGENT
Q) Express 3 sin x + 4 cos x in the form R cos (x-a) a is alpha

any idea i think we must change the sinx into cos x (Worried) - Apr 10th 2008, 10:41 AMbobak
This problem can easily be solved my comparing coefficients.

First start by stating your identity.

$\displaystyle R \cos(x - \alpha) \equiv 3 \sin x + 4 \cos x $

It is important that you understand exactly what $\displaystyle \equiv$ means before you go ahead, if you don't just say.

Expand the left hand side using the compound angle formula.

$\displaystyle R \cos x \cos \alpha + R \sin x \sin \alpha \equiv 3 \sin x + 4 \cos x $

compare coefficients to get

$\displaystyle R \cos \alpha = 4 $

$\displaystyle R \sin \alpha = 3 $

do you want to try and finish off form here ?

let me know how it goes form here.

Bobak - Apr 10th 2008, 10:44 AMmanutd4life
oh ok i forget wat its mean

(how u post these sign [alpha and other]) - Apr 10th 2008, 11:02 AMmanutd4life
- Apr 10th 2008, 11:03 AMbobak
you forget what $\displaystyle \equiv$, it should be covered somewhere in your textbook. It means that both sides of the expression are equal for all values of x. that is to say that the left hand side is identical to the right hand side.

If two expressions are identical then the coefficients $\displaystyle \sin x $ and $\displaystyle \cos x $ respectively are the same. the coefficient of $\displaystyle \sin x $ on the left hand side is $\displaystyle R \sin \alpha $ and on he right hand side it is 3.

are you following ?

Bobak - Apr 10th 2008, 11:16 AMmanutd4life
is this answer good:

$\displaystyle 5 \cos(x - 36.9) $ - Apr 10th 2008, 11:20 AMbobak
- Apr 10th 2008, 11:24 AMmanutd4lifeQuote:

Just remember that is for an angle in degrees. Do you know how to adjust the result for radians ?

Bobak

(another question)

can u help me in one more question?? - Apr 10th 2008, 11:30 AMbobak