1. Trigonometric Identity

So I have a question that is:

Given that cos theta = 24/25 and theta is in Quadrant I, determine sin 2theta, cos 2theta and tan 2theta. Which quadrant is 2theta in?

I already solved the sin, cos and tan portion of the problem

sin 2theta = 336/625
cos 2theta = 527/625
tan 2theta = 336/527

but the issue I have is I have no idea how to determine which quadrant 2theta is in.

Any help would be appreciated! Thanks in advance!

2. Re: Trigonometric Identity

$sin(2\theta)>0$
$cos(2\theta)>0$
$tan(2\theta)>0$

What does each of these inequalities tell you about $2\theta$?

3. Re: Trigonometric Identity

Too be honest I am not really sure >.<

that 2 theta is positive?

4. Re: Trigonometric Identity

It might help if you consider $2\theta$ as a single variable. That is, let $2\theta=a$ (a is for angle!) Now, each of the values you calculated is positive.

What quadrants can a be in to make sin(a) positive?
What quadrants can a be in to make cos(a) positive?
What quadrants can a be in to make tan(a) positive?

5. Re: Trigonometric Identity

oh I get it .. so Quadrant I. Because sin, cos and tan are all positive in Quadrant I