How many values of $\theta$ satisfy $2\cos(3\theta-1) = 0$, where $-\pi \le \theta \le \pi$?

Question

parthkohli · Answer

Divide both sides by $2$, and you get$$\cos(3\theta - 1) = 0$$For what all angles is cosine zero?

geerky42 · Answer

I got 2 but the answer is 6. I don't understand...

parthkohli · Answer

Consider the graph of $\cos(x)$.

geerky42 · Answer

$\dfrac{\pi}{2}$ and $-\dfrac{\pi}{2}$

parthkohli · Answer

You're right! o.O

geerky42 · Answer

so 3θ−1 got to be equal to either $\dfrac{\pi}{2}$ or $-\dfrac{\pi}{2}$

so i found 2 values theta can be, but key answer said 6...

parthkohli · Answer

$$\cos(3\theta - 1) = \cos(1 - 3\theta) = 0$$

parthkohli · Answer

Now, do you get it? ;-)

mertsj · Answer

I you want all the  theta answers between pi and -pi, you must find all the 3theta answers between 3pi and -3pi

geerky42 · Answer

Wait, I dont get it...

parthkohli · Answer

What Mertsj said is what I wanted to eventually point out...

parthkohli · Answer

I don't want to gobble this for you, but there's this thing called "frequency", which decreases when you increase the coefficient of $\theta$.

parthkohli · Answer

So if the graph of cosine is like|dw:1364057427035:dw|It'd become|dw:1364057444338:dw|More close to each other.