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 $\displaystyle a^2 + b^2 < c^2$, show that
$\displaystyle a \cos \theta + b \sin \theta = c$ has no real roots."
Let $\displaystyle x = \sin \theta$, so $\displaystyle \cos \theta = \sqrt{1 - x^2}$.
Then the equation becomes
$\displaystyle a \sqrt{1 - x^2} + b x = c$
so
$\displaystyle a \sqrt{1 - x^2} = c - bx$
squaring both sides,
$\displaystyle a^2 (1 - x^2) = (c - bx)^2$
You now have a quadratic equation in x. Find the discriminant of the equation and I think you will see the solution.