anonymous
  • anonymous
if cos(t)=-1/5 and pi
Precalculus
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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zepdrix
  • zepdrix
|dw:1362772905106:dw|Understand why I drew that triangle in the third quadrant?
anonymous
  • anonymous
not quite sure why?
zepdrix
  • zepdrix
|dw:1362773055192:dw| They told us that the angle t in within this interval.\(\large \pi

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anonymous
  • anonymous
ok now i understand that part
zepdrix
  • 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
  • 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
  • anonymous
|dw:1362773386830:dw|
zepdrix
  • 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
  • anonymous
opposite will equal 4?
anonymous
  • anonymous
sorry did an error......missing side equals to \[+/- 2\sqrt{6}\]
zepdrix
  • 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
  • anonymous
we want a negative answer because tan is only positive in the 3rd Q
zepdrix
  • 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
  • zepdrix
Ok good. Everything is labeled correctly. Just have to find \(\large \csc t\) now! :)
anonymous
  • anonymous
hypotenuse over opposite
zepdrix
  • zepdrix
yepppppp
anonymous
  • anonymous
5/-2sqrt6
zepdrix
  • zepdrix
yay good job! \c:/
zepdrix
  • 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
  • anonymous
5sqrt6/-12?
zepdrix
  • zepdrix
Yes.
anonymous
  • anonymous
a little confused on the denominator part....not sure if its 12 or not
zepdrix
  • zepdrix
\[\large 2 \cdot \sqrt6 \sqrt6 \qquad = \qquad 2\cdot6 \qquad = \qquad 12\]Hmm yah everything looks ok there!
anonymous
  • anonymous
ok thanks!!!
anonymous
  • anonymous
thanks for the help some time a 8am class only aborbs so much in an hour and with 300 classmates lol
zepdrix
  • zepdrix
heh ill bet! XD

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