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

Question

if cos(t)=-1/5 and pi<t<3pi/2. find csc(t)

zepdrix · Answer

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

anonymous · Answer

not quite sure why?

zepdrix · Answer

|dw:1362773055192:dw|      They told us that the angle t in within this interval.$\large \pi<t<3\pi/2$. So we draw a line in the third quadrant and form a triangle from it.

anonymous · Answer

ok now i understand that part

zepdrix · Answer

|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 · Answer

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

anonymous · Answer

|dw:1362773386830:dw|

zepdrix · Answer

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 · Answer

opposite will equal 4?

anonymous · Answer

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

zepdrix · Answer

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 · Answer

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

zepdrix · Answer

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|