In Exercises 9–16, evaluate the trigonometric function at the qua...

Question

In Exercises 9–16, evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined.cot 𝜋2

Accepted Answer

Hello, today we're going to be finding the value of the following trigonometric function. So what we are given is cotangent of three pi over two. Now, in order to solve this problem, we're going to need to take a look at the unit circle. So let's draw a unit circle. Now, what we need to do is we need to identify the location of our given angle. The given angle in this case is three pi over two, three pi over two is located at the degree mark of the unit circle. And the terminal point for this given angle is given to us as zero comma negative one. Now keep in mind that any point found along the unit circle is defined as cosine theta comma sine theta. What this means is that cosine represents any X value along the unit circle and sine represents any Y value on the unit circle. But notice that the unit circle does not use any values of cotangent in its points. So how can we use the unit circle to figure out the value of cotangent at three pi over two? Well, we have a Pythagorean theorem to help us rewrite cotangent in terms of cosine and sine, the identity for cotangent is given to us as cotangent data is equal to cosine data overs sign data. And so if we use this identity, we can rewrite the given trigonometric function in terms of sign and cosine. So using this identity cotangent of three pi over two can be rewritten as cosine three pi over two over sign of three pi over two. Now, what we're going to need to do is we're going to need to figure out the following values for cosine at three pi over two and sign of three pi over two. Well, we already have those values from the given terminal point on the unit circle. Recall that cosine is every X value and sine is every Y value and looking at the unit circle, what this means is that cosine of three pi over two is going to equal to zero and sign of three pi over two is going to equal to negative one. So if we plug this in what we can replace cosine three pi over two with is zero. And what we replace sine three pi over two with is negative one. Now zero, divided by any value is going to equal to zero. And what this means is that cotangent of three pi over two is going to equal to zero. This is going to be the value for the given trigonometric function. And with that being said, the answer to this problem is going to be c so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

In Exercises 9–16, evaluate the trigonometric function at the quadrantal angle, or state that the expression is undefined.cot 𝜋2

Key Concepts

Quadrantal Angles

Cotangent Function

Undefined Expressions in Trigonometry

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