1. ## Revision Questions

Hey guys

Could someone please explain to me how to do these questions? I can't seem to b able to figure them out. Thanx!

2. Originally Posted by xwrathbringerx
Hey guys

Could someone please explain to me how to do these questions? I can't seem to b able to figure them out. Thanx!
I'll try #3:

"If $a^2 + b^2 < c^2$, show that
$a \cos \theta + b \sin \theta = c$ has no real roots."

Let $x = \sin \theta$, so $\cos \theta = \sqrt{1 - x^2}$.

Then the equation becomes
$a \sqrt{1 - x^2} + b x = c$

so

$a \sqrt{1 - x^2} = c - bx$

squaring both sides,

$a^2 (1 - x^2) = (c - bx)^2$

You now have a quadratic equation in x. Find the discriminant of the equation and I think you will see the solution.