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# What is the value of cscθ? (Work is shown)

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The terminal ray of angle θ drawn in standard position passes through (1,−3).

What is the value of cscθ?

cscθ =

Here's my work:

1) I plotted (1, -3) on a graph and then drew a point from the orgin.

2) Then drew from the point (1, -3) straight up to the x axis, so it forms a right triangle.

3) From there, I calculated the length of each leg of the triangle by using the pythagorean theorem.

- the shortest leg 1 unit

- the one longer than it is 3 units

- the hypotenuse is 3.16227766 ( I rounded it to 3.16)

4) To get the value of cscθ, I used my knowledge that cscθ is hypotenuse over opposite.

This is where I got confused. I'm havin a hard time determining which angle it's actually asking for. Is cscθ the angle near the orgin or the one from the point given?

I also don't really know what it means by simplest form. Does that mean fraction or decimal? Or something else perhaps?

If someone could help me, I'd appreciate that a lot:) Thank you!

Jun 10, 2020
edited by auxiarc  Jun 10, 2020

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Okay, so I did it both ways and I think based off of my knowledge, it is more logical for it to be the angle near the orgin, because if it was the other one, it would be 17 degrees, which is obviously not the answer, because that would make the third angle obtuse, and it isn't.

Jun 10, 2020
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Doing the math, I did cscθ = 3.16/3 and I got 71.56 degrees.

Now the only part I'm confused about is what it means by simplest form lol

auxiarc  Jun 10, 2020
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Nevermind, I got it. But thanks. :)

Jun 10, 2020