# Help with Double Angle Identities!!!

• Nov 27th 2012, 03:46 PM
whittwhitt
Help with Double Angle Identities!!!
cos θ = 24/25

The angle lies in quadrant 1; 0<θ<90

Find sin2θ

I know you would use either the formula cos^2θ - sin^2θ or 2sinθcosθ
And I know that the answer is 339/625, but I do not know how to get that answer?
• Nov 27th 2012, 04:39 PM
topsquark
Re: Help with Double Angle Identities!!!
Quote:

Originally Posted by whittwhitt
cos θ = 24/25

The angle lies in quadrant 1; 0<θ<90

Find sin2θ

I know you would use either the formula cos^2θ - sin^2θ or 2sinθcosθ
And I know that the answer is 339/625, but I do not know how to get that answer?

Well, you know sin(theta) since you know cos(theta). And sin(2theta) = 2 sin(theta) cos(theta)....

-Dan
• Nov 27th 2012, 04:39 PM
HallsofIvy
Re: Help with Double Angle Identities!!!
Yes, you use one of those but which? One is $\displaystyle sin(2\theta)$ and which is $\displaystyle cos(2\theta)$? (What happens if $\displaystyle \theta= 0$?)

If $\displaystyle cos(\theta)= 24/25$ and $\displaystyle \theta$ is in the first quadrant what is $\displaystyle sin(\theta)$? (You do know that $\displaystyle sin^2(\theta)+ cos^2(\theta)= 1$, don't you?
• Nov 27th 2012, 04:41 PM
zhandele
Re: Help with Double Angle Identities!!!
Let me see ... is your difficulty that you work the problem out, but you get an answer different from 339/625?

If so, maybe you answer is right. I also get something different from 339/625.

• Nov 27th 2012, 04:52 PM
whittwhitt
Re: Help with Double Angle Identities!!!
My teacher gave us the answers so that we could check to see if we were doing the problem right.
• Nov 27th 2012, 04:57 PM
zhandele
Re: Help with Double Angle Identities!!!
Well, he might've made a typo or something. What answer do you get?
• Nov 27th 2012, 05:08 PM
whittwhitt
Re: Help with Double Angle Identities!!!
Could you guys help me with one more problem? ... I promise I wrote this one down correctly

Thank you!

Could you help me with another problem?

secθ = -(sqrt41)/4
In quadrant 3; cosθ > 0
Find sin2θ
• Nov 27th 2012, 05:13 PM
zhandele
Re: Help with Double Angle Identities!!!
This is the same kind of problem as the last one. Only you say cos(theta) > 0? In quadrant III, cos < 0, or so I believe. Am I wrong? Do you mean that cos(2 theta) > 0?

Oh, I see. You mean that sin(theta) < 0. In quadrant 3 both functions > 0. That means theta > pi, so 2*theta > 2pi, the answer is probably in quadrant 1. You'd expect the sin(2 theta) to be > 0, right?
• Nov 27th 2012, 05:49 PM
zhandele
Re: Help with Double Angle Identities!!!
I have to go to sleep now, but do you know the first step to take? I'll give you a hint if not.