if cos(t)=-1/5 and pi

Precalculus
- anonymous

if cos(t)=-1/5 and pi

Precalculus
- chestercat

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- zepdrix

|dw:1362772905106:dw|Understand why I drew that triangle in the third quadrant?

- anonymous

not quite sure why?

- zepdrix

|dw:1362773055192:dw| They told us that the angle t in within this interval.\(\large \pi

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## More answers

- anonymous

ok now i understand that part

- zepdrix

|dw:1362773145892:dw|Let's look at just the triangle now. Don't worry about the fact that I labeled the angle \(\large t'\). That's not super important. Just think of it as \(\large t\).

- zepdrix

\(\large \cos t=-\dfrac{1}{5}=\dfrac{adjacent}{hypotenuse}\)
So how would we label these sides?
HINT: We always let the hypotenuse be positive.

- anonymous

|dw:1362773386830:dw|

- zepdrix

Ok looks good!
Just need to find the missing side using the `Pythagorean Theorem` and then we just have one small step after that.

- anonymous

opposite will equal 4?

- anonymous

sorry did an error......missing side equals to \[+/- 2\sqrt{6}\]

- zepdrix

Ok looks good.
Now remember that we drew our triangle in the `third` quadrant.
So for that OPPOSITE leg, did we move UP or DOWN?
Do we want the positive or negative answer?

- anonymous

we want a negative answer because tan is only positive in the 3rd Q

- zepdrix

Haha that's an interesting way to think about it XD
I was thinking about the fact that we moved downward in the y direction to make the opposite length. So it would be negative. But whatever works for you! :D|dw:1362773803586:dw|

- zepdrix

Ok good. Everything is labeled correctly. Just have to find \(\large \csc t\) now! :)

- anonymous

hypotenuse over opposite

- zepdrix

yepppppp

- anonymous

5/-2sqrt6

- zepdrix

yay good job! \c:/

- zepdrix

For your final answer it might be a good idea to `rationalize` your answer.
Get the irrational number out of the denominator.
Multiply the top and bottom by sqrt6.

- anonymous

5sqrt6/-12?

- zepdrix

Yes.

- anonymous

a little confused on the denominator part....not sure if its 12 or not

- zepdrix

\[\large 2 \cdot \sqrt6 \sqrt6 \qquad = \qquad 2\cdot6 \qquad = \qquad 12\]Hmm yah everything looks ok there!

- anonymous

ok thanks!!!

- anonymous

thanks for the help some time a 8am class only aborbs so much in an hour and with 300 classmates lol

- zepdrix

heh ill bet! XD

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