factorising trigonometric function

• Mar 18th 2013, 08:35 AM
tomoshaw
factorising trigonometric function
for -180 </= θ </= 180, solve

3sin^2(θ) - sin(θ)cos(θ) - 4cos^2(θ) = 0

i can't factorise the middle term to separate the sine and cosine
• Mar 18th 2013, 09:21 AM
Plato
Re: factorising trigonometric function
Quote:

Originally Posted by tomoshaw
for -180 </= θ </= 180, solve
3sin^2(θ) - sin(θ)cos(θ) - 4cos^2(θ) = 0
i can't factorise the middle term to separate the sine and cosine

Oh, come on. You can factor $3x^2-xy-4y^2~?$
• Mar 18th 2013, 09:28 AM
Shakarri
Re: factorising trigonometric function
Let $sin\theta=x$ and $cos\theta=y$

Substitute these into the equation and you get
$3x^2-xy-4y^2$

Edit: Plato beat me to it.
• Mar 18th 2013, 09:31 AM
tomoshaw
Re: factorising trigonometric function
This is how i originally tried to tackle it. I'm either blind or I need to be posting on a key stage 2 board but i just can't see how that factorises and I know it's really simple.
• Mar 18th 2013, 09:42 AM
tomoshaw
Re: factorising trigonometric function
i see it factorises to

(3x-4y)(x+y)

but i thought you could only have 1 trigonometric term in each factor?
• Mar 18th 2013, 04:26 PM
Prove It
Re: factorising trigonometric function
No, you can have whatever is needed in each factor. Now by setting each factor equal to 0, you end up with two simpler equations to solve for theta.