# Math Help - Trigonometric Equation

1. ## Trigonometric Equation

Hi again x.x

I'm having a huge problem with these, here goes:

It is given that a=2sinθ + cosθ and b=2cosθ + sinθ where
θ 360°

(i) Show that a
² + b ² is constant for all values of θ
(ii) Given that 2a = 3b show that tanθ = 4/7 and find the corresponding values of θ

My answer for (i): 5sin
²θ + 5cos²θ = θ by adding A and B squared.

For (ii) I don't understand the question.

Also, could someone point me to a website containing detailed explainations and examples of these? I feel like I only half understand them :/

Thanks again guys

2. You've been given a and b, so you can construct 2a and 3b and see what the equation gives you:

$2 (2 \sin \theta + \cos \theta) = 3 (2 \cos \theta + \sin \theta)$

simplifying that down you get:

$4 \sin \theta + 2 \cos \theta = 6 \cos \theta + 3 \sin \theta$

$4 \sin \theta - 3 \sin \theta = 6 \cos \theta - 2 \cos \theta$

$\sin \theta = 4 \cos \theta$

$\frac {\sin \theta}{\cos \theta} = \tan \theta = 4$

... which is not the answer I was expecting, I was expecting it to be 4/7.

Did you copy the question right?

3. a=2sinθ + cosθ and b=2cosθ + sinθ

No indeed .. *
b=2cosθ - sinθ

It works out perfectly when you change the sign >.o