For what value of theta between 0 and 2pi is cot=0 and sin< 0?

tcutu

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I may be over-thinking this, but I am thoroughly confused. Okay, so the question is:

For what value of theta between 0 and 2pi is cot=0 and sin< 0?

From SOH-CAH-TOA I know that sine is opposite/hypotenuse and cot is the opposite of tangent so it's adjacent/opposite. So pulling out my unit circle I start thinking about special triangles and try to work with 30-60-90 and 45-45-90 looking for the combination of adjacent and opposite's that will equal 0. I was trying to use the degrees in the special triangles. For example: the cot of 45 is 1/1, for 60 its 1/root of 3, and for 30 it's root of 3/1. Obviously none of those equal zero and I don't know where to go from there. Help?
 
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Okay, so the question is: For what value of theta between 0 and 2pi is cot=0 and sin< 0?

\(\displaystyle \cot \left( {\dfrac{{3\pi }}{2}} \right) =~?\)

\(\displaystyle \sin \left( {\dfrac{{3\pi }}{2}} \right) =~?\)
 
Can you explain in words please? I was very ill and missed about a week of pre-calc and these numbers aren't making sense to me.
 
Can you explain in words please? I was very ill and missed about a week of pre-calc and these numbers aren't making sense to me.
There is nothing to explain.
You are expected to know that \(\displaystyle \cot \left( \theta \right) = \dfrac{{\cos \left( \theta \right)}}{{\sin \left( \theta \right)}}\)
You are also expected to know the functions of common measures such as \(\displaystyle \dfrac{3\pi}{2}\).

It is not our purpose to give you a tutorial.
 
Can you explain in words please? I was very ill and missed about a week of pre-calc and these numbers aren't making sense to me.
Stop thinking in degrees with calculus; use radians instead. Thinking unit circle is wise. And of course you understand that the trig functions are cyclic, which means that we frequently think about them over a limited domain such as \(\displaystyle 0 \le \theta \le 2 \pi .\)[FONT=MathJax_Main]
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Basic trig identities: \(\displaystyle cot( \theta ) = \dfrac{1}{tan ( \theta )}\ and\ tan( \theta ) = \dfrac{sin( \theta )}{cos ( \theta )} \implies cot ( \theta ) = \dfrac{cos ( \theta )}{sin ( \theta )}.\)

With me so far?

So if \(\displaystyle cot( \theta ) = 0,\) what does \(\displaystyle cos( \theta ) =\ ?\)

In radians, for what values of \(\displaystyle \theta\ does\ cos( \theta ) = 0,\ given\ 0 \le \theta \le 2\pi ?\)

In radians, for what values of \(\displaystyle \theta\ does\ sin( \theta ) < 0,\ given\ 0 \le \theta \le 2\pi ?\)
 
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Okay I think I get you're saying, JeffM. I keep trying to work with degrees and forgetting that I have to use radians (which is a bit foreign to me right now to be honest). Thank you!
 
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