# How many solutions of the trig functions

• Oct 27th 2009, 11:27 AM
Aquafina
How many solutions of the trig functions
The simultaneous equations in x,y

xcosθ - ysinθ = 2
xsinθ + ycosθ = 1

are solvable for how many values of θ in the range 0<= θ < 2pi

I was told that it is for all values, using the idea of discriminants. But I haven't learnt this yet, so I am meant to use some other method. Any advice?

Thanks
• Oct 27th 2009, 02:37 PM
Quote:

Originally Posted by Aquafina
The simultaneous equations in x,y

cosθ x - sinθ y = 2
sinθ x + cosθy = 1

are solvable for how many values of θ in the range 0<= θ < 2pi

I was told that it is for all values, using the idea of discriminants. But I haven't learnt this yet, so I am meant to use some other method. Any advice?

Thanks

Are x and y meant to be part of the angle? If not, I think it would be best to write this as:

$xcos(\theta)-ysin(\theta)=2$

$xsin(\theta)+ycos(\theta)=1$
• Oct 27th 2009, 09:50 PM
Aquafina
Ok I edited them. Any advice on it?