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mattlai7
 2 years ago
if cos(t)=1/5 and pi<t<3pi/2. find csc(t)
mattlai7
 2 years ago
if cos(t)=1/5 and pi<t<3pi/2. find csc(t)

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zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1362772905106:dwUnderstand why I drew that triangle in the third quadrant?

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw: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.

mattlai7
 2 years ago
Best ResponseYou've already chosen the best response.0ok now i understand that part

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1dw:1362773145892:dwLet'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
 2 years ago
Best ResponseYou've already chosen the best response.1\(\large \cos t=\dfrac{1}{5}=\dfrac{adjacent}{hypotenuse}\) So how would we label these sides? HINT: We always let the hypotenuse be positive.

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Ok looks good! Just need to find the missing side using the `Pythagorean Theorem` and then we just have one small step after that.

mattlai7
 2 years ago
Best ResponseYou've already chosen the best response.0opposite will equal 4?

mattlai7
 2 years ago
Best ResponseYou've already chosen the best response.0sorry did an error......missing side equals to \[+/ 2\sqrt{6}\]

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Ok 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?

mattlai7
 2 years ago
Best ResponseYou've already chosen the best response.0we want a negative answer because tan is only positive in the 3rd Q

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Haha 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! :Ddw:1362773803586:dw

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1Ok good. Everything is labeled correctly. Just have to find \(\large \csc t\) now! :)

mattlai7
 2 years ago
Best ResponseYou've already chosen the best response.0hypotenuse over opposite

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1For 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.

mattlai7
 2 years ago
Best ResponseYou've already chosen the best response.0a little confused on the denominator part....not sure if its 12 or not

zepdrix
 2 years ago
Best ResponseYou've already chosen the best response.1\[\large 2 \cdot \sqrt6 \sqrt6 \qquad = \qquad 2\cdot6 \qquad = \qquad 12\]Hmm yah everything looks ok there!

mattlai7
 2 years ago
Best ResponseYou've already chosen the best response.0thanks for the help some time a 8am class only aborbs so much in an hour and with 300 classmates lol
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