Thread: Help with Double Angle Identities!!!

1. 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?

2. Re: Help with Double Angle Identities!!!

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

3. 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?

4. 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.

5. 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.

6. Re: Help with Double Angle Identities!!!

Well, he might've made a typo or something. What answer do you get?

7. 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

8. 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?

9. 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.