# Thread: Having trouble figuring out a trig problem

1. ## Having trouble figuring out a trig problem

It has been like a year since I took pre-calculus. Now were in the review section and were reviewing trig and I am struggling remembering much about the rules. In any case here is my problem:

Find cos(theta) and tan(theta) if sin(theta)=5/13 and (now here is the part throwing me off) 0 <= theta <= pie/2

I found that cos(theta)=194/13 and tan(theta)=5/194 I typed these answers in, and they were wrong. I am not sure why but I am almost positive it has something to do with the stipulation <= theta <= pie/2. Could someone please (not only show me the answers) but also explain how to deal with these types of stipulations?

2. ## Re: Having trouble figuring out a trig problem

no way $\displaystyle \cos{\theta} = \frac{194}{13}$ ... why?

since $\displaystyle \theta$ resides in quad I , all three trig ratios are positive.

us the following identities ...

$\displaystyle \cos^2{\theta} + \sin^2{\theta} = 1$

$\displaystyle \tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}$

... try it again.

3. ## Re: Having trouble figuring out a trig problem

if $\displaystyle \sin(\theta) = \frac{5}{13}$, then you have a right triangle with hypotenuse of length 13, and vertical leg of length 5. how do you find the length of the third leg (hint: pythagoras)?

4. ## Re: Having trouble figuring out a trig problem

OMG lol im sorry haha what I did for some reason was say that since sin(theta)= 5/13 that meant that I could say 5^2 + 13^2 = 194 or an adjacent side of a right triangle. I was off so cos = 12/13 and tan is 5/12 lol thanks for your help!

5. ## Re: Having trouble figuring out a trig problem

Originally Posted by Deveno
if $\displaystyle \sin(\theta) = \frac{5}{13}$, then you have a right triangle with hypotenuse of length 13, and vertical leg of length 5. how do you find the length of the third leg (hint: pythagoras)?
Wait I thought that is what I did orignally and I came up with 194 since sin is opp/hyp then I took 5^2 + 13^2 = 194 and said that was my adj side... where did i go wrong?

6. ## Re: Having trouble figuring out a trig problem

adjacent side = $\displaystyle \sqrt{hyp^2 - opp^2}$ = $\displaystyle \sqrt{13^2 - 5^2}$

btw ... next time post trig questions in the trig forum.

7. ## Re: Having trouble figuring out a trig problem

Ok I did get the right answers so thanks for the help guys but I am still confused. Since 13^2 + 5^2 = 194 then I square 194 but when I do that I don't get the whole number 13 my calc says its 13.928... which rounded is 14 however the answer for cos was 12/13... why would it not round up instead of down?

P.S. I do plan on sticking around so I will post all of my questions in the correct section from now on.

8. ## Re: Having trouble figuring out a trig problem

Arrgh. That is NOT using the Pythgorean theorem. The Pythagorean theorem says that the sum of the squares of the two legs is the square of the hypotenuse. Here, you have one leg of length 9 and the hypotenuse of length 13. Writing the length of the unknown leg as "x", the Pythagorean theorem says that $\displaystyle x^2+ 5^2= 13^2$ so that $\displaystyle x^2= 13^2- 5^2= 169- 25= 144$.