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Doglover2011 · Oct 7, 2009, 11:35 AM

I'm trying to study for an upcoming test and was doing this problem:

Find the values of the other five trig functions given that sin= 1/2, pi/2<Theta<Pi

I have found all but 2 functions, Tan and Cot. I am not sure which formula to use for this. Any suggestions?

Unknown008 · Oct 7, 2009, 11:39 AM

I don't quite understand what you have to do. Could you post the answers you already got?

Doglover2011 · Oct 7, 2009, 12:01 PM

We have to find the other functions-sine, cosine, etc.

Here are my answers(I hope they are right hehe but I think they are):

Sine-1/2
Csc-2
Cos-square root of 3/2
Sec-2times square of 3/3

Now I just need to figure out how to get Tan, because Cot will be the recp. Of Tan. I need to use an identity, I just don't know which one. I don't see any with just sine and Tan.

Doglover2011 · Oct 7, 2009, 12:03 PM

and we are suppose to use the given (1/2 sine) to figure it out.

But I wonder if I could use

Sin(1/2)^2+Cos^2Theta=1?

ArcSine · Oct 7, 2009, 12:53 PM

Be careful with your signs. The fact that the angle $\theta$ lies between $\frac{\pi}{2}$ and $\pi$ tells you you're dealing with a Quad II angle. Sine is certainly positive there, but cosine is..

As to Tan, just remember that by definition $tan\ \theta \ = \ \frac{\text{sin}\theta}{\text{cos}\theta}$ . So once you've got sine and cosine in hand, tan is a cakewalk. After that, nail down the other three using the reciprocal identities.