Find the trigonometric values of theta.

• Feb 14th 2011, 05:28 PM
dagbayani481
Find the trigonometric values of theta.
My teacher wasn't very thorough with the lesson and I'm pretty lost on how to go about doing this.

Basically I have to find all of the trigonometric values of the following:

$\tan \theta = -4 , \sin \theta > 0$

What steps do I need to take in order to find sin, cos, tan, csc, sec, and cot using the following information?
• Feb 14th 2011, 06:14 PM
Soroban
Hello, dagbayani481!

Quote:

$\tan \theta = \text{-}4 ,\;\;\sin \theta > 0$

$\text}Find all of the trignometric values of }\theta.$

We know that tangent is negative in quadrants 2 and 4.
We know that sine is positive in quadrants 1 and 2.
. . Hence, $\,\theta$ is in quadrant 2.

Code:

          *           \             \             \ @       - - - - * - - -

We know that: . $\tan\theta \:=\:-\dfrac{4}{1} \:=\:\dfrac{opp}{adj}$

So the diagram looks like this:

Code:

          *           |\         4 | \           |  \ @       - - * - * - - -           -1

We have: . $opp = 4,\;adj = \text{-}1$

Pythagorus says: . $hyp \:=\:\sqrt{4^2 + (\text{-}1)^2} \:=\:\sqrt{17}$

Now you can write all six trigonometric values.

• Feb 14th 2011, 10:09 PM
dagbayani481
Thanks that really helped!

I tried working it out myself before I saw the answer. I got something similar except instead of having the opp. side as 4 and the adj. side as -1, I had the opp. side as -4 and the adj. side as 1. Does it make a difference where you chose to put the negative?
• Feb 15th 2011, 01:10 AM
pickslides
Quote:

Originally Posted by dagbayani481
Does it make a difference where you chose to put the negative?

It does as that would put this triangle in either the 3rd or 4th quadrant.

But in this case you could get away with it as it would not change the result.
• Feb 15th 2011, 04:56 AM
HallsofIvy
Yes, it does change the result. If you take "opposite side" as -4 and "near side" as +1, you get the sine, "opposite over hypotenuse" negative when the probelem specifically says it is positive. You would have the wrong signs for sine, cosine, secant, and cosecant.