In Exercises 9–16, use the given triangles to evaluate each expre...

Question

In Exercises 9–16, use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.

cot 𝜋/3

Accepted Answer

Hello, everyone. We are asked to use the given triangle to find the value of the expression and rationalize the denominator of the final answer. If required, we are given a right triangle. P. QR with the right angle at angle Q angle P is degrees angle R is 60 degrees side, P Q measures radical three side. QR measures one. And our hypo pr measures two, we are asked to find the value of the cotangent of pi divided by six. We are given four answer choices. First, I'm gonna see what I recall about co tangent. So we have the cotangent of pi divided by six. I know that cotangent is the reciprocal of tangent and that this should be the adjacent side divided by the opposite side. But opposite of what pi divided by six doesn't straight tell me 30 degrees or 60 degrees. So I need to first take my radiant measure of pi divided by six and change it into degrees. I can do so by recalling that pie is approximately equivalent to 100 80 degrees. So I can say this is 180 degrees divided by six at which point I know that Pi divided by six is equivalent to degrees. So now I'm gonna find the cotangent of 30 degrees. Again, I'm gonna use the side that is adjacent to it divided by the side that is opposite to it. 30 degrees is at angle P. So adjacent to angle P is the leg radical three, an opposite would be the side with the leg measure of one radical three divided by one is radical three. So the cotangent of pi divided by six is radical three which is answer choice C have a nice day.

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In Exercises 9–16, use the given triangles to evaluate each expression. If necessary, express the value without a square root in the denominator by rationalizing the denominator.
cot 𝜋/3