# R formulae (double angle formulae) URGENT

• Apr 10th 2008, 10:33 AM
manutd4life
R 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 AM
bobak
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 AM
manutd4life
oh ok i forget wat its mean

(how u post these sign [alpha and other])
• Apr 10th 2008, 11:02 AM
manutd4life
Quote:

Originally Posted by bobak
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

forget wat this $\displaystyle \equiv$ means

explain brief how u compare these coefficient to get

$\displaystyle R \cos \alpha = 4$
$\displaystyle R \sin \alpha = 3$

quick plz
• Apr 10th 2008, 11:03 AM
bobak
Quote:

Originally Posted by manutd4life
oh ok i forget wat its mean

(how u post these sign [alpha and other])

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 AM
manutd4life

$\displaystyle 5 \cos(x - 36.9)$
• Apr 10th 2008, 11:20 AM
bobak
Quote:

Originally Posted by manutd4life

$\displaystyle 5 \cos(x - 36.9)$

(Clapping) Well done.

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

Bobak
• Apr 10th 2008, 11:24 AM
manutd4life
Quote:

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

Bobak
No dont how

(another question)
can u help me in one more question??
• Apr 10th 2008, 11:30 AM
bobak
Quote:

Originally Posted by manutd4life
No dont how

(another question)
can u help me in one more question??

Well if you haven't covered radians in school yet it is not important (yet).