Question 549783: Hello, I am trying to find the exact function value of: cotangent negative 17 pie over 3. I multipled 17 by 180 and divided that by three, but after that I'm not too sure what to do after that. Do I subtract 360? That was my next guess, but not too sure. Hoping you could help!
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
The tree you are barking up is not only the wrong tree, it is in the totally wrong part of the forest.
Let's begin again.
The periodicity of cotangent is  , hence \ =\ \cot\left(\varphi\right)) where  . So let  , then:
\ =\ \cot\left(\frac{\pi}{3}\right))
We also know that
\ =\ \frac{\cos\left(\vartheta\right)}{\sin\left(\vartheta\right)})
Then, looking at the unit circle:
where we recall that the value of  is the  -coordinate of the intersection of the terminal ray of the angle and the unit circle and the  is the  -coordinate of the same point, we can determine:
)
and
)
Divide and rationalize the denominator to obtain:
\ =\ \cot\left(\frac{\pi}{3}\right)\ =\ \frac{\cos\left(\frac{\pi}{3}\right)}{\sin\left(\frac{\pi}{3}\right)}\ =\ \frac{\sqrt{3}}{3})
One more thing. "pie" is a prepared food item consisting, generally, of a more or less flakey crust filled with some sort of sweet, often fruit based, filling in the case of pies created as a dessert course, or savory filling in the case of those created as either a main or side dish. "pi" is the romanization of the lower case Greek alphabet character representing the ratio of a circle's circumference to its diameter.
John
My calculator said it, I believe it, that settles it
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