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1.44.23Without using calculator; evaluate the following expression or state that the quantity is undefined . 291 cot...

Question

1.44.23Without using calculator; evaluate the following expression or state that the quantity is undefined . 291 cot

1.44.23 Without using calculator; evaluate the following expression or state that the quantity is undefined . 291 cot



Answers

Evaluate the following expressions or state that the quantity is undefined. $$\cot (-17 \pi / 3)$$

Hello students in this question we have to find the exact value of God of arc court minus through three. So firstly are caught minus through three will be some angle and it will be the angle whose port engine value is minus through three. So let me write, let art court minus rule three. Let this angle B. T. So according to to the basic definition of Are 10x. Function. We can say that poor tangent of tea here Is negative of 2 3. Let the let the speak with the # one. Now we have to find the value of part of Are caught negative rule three And we assume this value equals two T. So the whole expression becomes caught of T. And from the first equation court of tea is nothing but rules three. So the final answer to this question is negative of Route three. I hope it's clear to you. Thank you.

Sewer back again. Back right off from where it started or where we left off. Gonna pick it up from where we left off. So this is still the unit circle intact. Eso contain unify right? Coup tangent of what is it? Definition of contingent is there's a reciprocal off is a reciprocal off Tangin. Right? And what is tangent Tan Yan design of a co sign. So the reciprocal is just gonna be a flip, Right? So co sign comes to the top and then sign comes to the bottom. That is a reciprocal. That is how you flip it, right? So all you gotta do is just fine. The two quantities, right? So we're here at ah, sign Pi zero here. Right, Remember? So this is the 2nd 1 is a sign. Uh, coordinate. And the 1st 1 is the co sang Courtney. So over here you have the coast on this coast and coordinate on a unit circle for pie. Is this one here? Right. Says one negative one, actually. And over now, the sign. Coordinate zero. Right. So you have in a negative infinity kind of thing. We just not at number right. Negative. Infinity is not a number, so we're going to say it is undivided. That is undefined.

Who want to find the co tangent of negative 13 pi over three. We want to start thinking about where that angle is. Well, negative 13. High over three. I think about it in degree measure. Let's see what it would be in degrees. Gonna multiply about 1 81 190 degrees over pat the past divide out. And so what I have is negative 13 times now. 1 80 divided by three is 60 degrees. And so I found out that negative 13 pi over three is the same. Angle is negative. 780 did Greece. Now let's come over to our to our our period are co ordinate period, and I'm sweeping out an idol in the negative direction. When I go full circle, that's negative. 3 60 and full circle again is negative. 7 20 and then I go 60 degrees more. Now here is my angle in quadrant, for I will drop that vertical line there. And I know that this is a 60 degree reference angle. You know, race those arcs just so I have room to right here. Let's see, Just erase the ark center in here so they're not in my way when I'm working the problem. I wanna look at this special right triangle. This is a 60 degree reference angle. See, I moved in the negative direction. So it is negative. 60 degrees in quadrant full. Well, it's a special right triangle, so that means this vertical distance has a length of square with three. And so the y coordinate of this point is negative. Square root of three. Then when I look at this horizontal segment, I can represent it with one. You can think that it's Gordon is being a one. This is if I'm on the unit circle. Well, um, now, on behalf partners would be to where we don't need that companies for to find our change. It I was keeping contains. We're finding co change, not change it near Almost wrote a t There are waning the co tangent. Coat engine is the reciprocal of changing. We want the co tangent. Uh, negative 13. Uh huh. Divided bath three. And so our co tangent is It's over. Why? So in this case, it would be one divided by a negative square root of three. Now, when we rationalize that denominator, that means we're gonna multiply by square to three in the top and bottom so we would have won. Times Square were 23 divided by negative square 123 terms square 123 So when we rationalize that denominated, what we're doing is we're getting the radical out of the denominator, a positive divided by negativism. Negatives are answer is negative. Square root of three divided.

The coach engine of pie is defined as one over the tangent of pie. This is also defined as co sign of time, divided by the sine. If I and here we can just use the unit circle to evaluate the coastline, a pie in the sign up I to get our answer for the code changer to pie. So the coastline of pie, which is the X coordinate of the point on the unit circle at PI ratings, which is negative one come zero. The X coordinate relates to the coast science this way. Negative one over the sign which relates to the Y coordinate, which is zero and year. We have division by zero that is not allowed division by zero, in other words, relates her results in a number that is undefined. So the co tension of pie is in fact, undefined.


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