In Exercises 61–86, use reference angles to find the exact value ...

Question

In Exercises 61–86, use reference angles to find the exact value of each expression. Do not use a calculator.tan 9𝜋2

Accepted Answer

Hello, today we're gonna be evaluating the following expression by using reference angles. So what we are given is tangent of 13 pi over two. Now, one thing to note is that 13 pi over two lies outside of one rotation of the unit circle. One rotation of the unit circle is defined from the angle 0 to pi. So what we want to do is we want to rewrite 13 pi over two in a standard form that lies between zero and two pi. In order to do this, we're going to take our given angle which is 13 pi over two and subtract one rotation of the unit circle which is two pi in this case. And we want to keep doing this until we get a radiant that lies between zero and two pi. So 13 pi over two minus two pi two pi can be rewritten as four pi over two. So we can rewrite this statement as 13 pi over two minus four pi over two. This is gonna leave us with nine pi over two. Then we're going to subtract two pie from this value as well. So nine pi over two minus four pi over two equals to five pi over two. And if we subtract one more rotation, again, we get five pi over two minus four pi over two, which is equal to pi over two. So this is the new angle in a standard form that lies between zero and two pi. And what this statement means is that tangent of 13 pi over two is equivalent to tangent of pi over two. Now where does Pi over two lie on the unit circle? Well, Pi over two is the 90 degree angle from the starting point of the unit circle. And the terminal point found at this at this angle is zero. Comma one recall that tangent is defined as our Y value over our X value here, our X value is zero and our Y value is one. So what this means is that tangent of Pi over two is equal to 1/0. But this is going to produce an undefined value, which means that tangent of Pi over two is undefined. And since tangent of 13 pi over two is equivalent to tangent of pi over two, that means that tangent of 13 pi over two is undefined. 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 61–86, use reference angles to find the exact value of each expression. Do not use a calculator.tan 9𝜋2

Key Concepts

Reference Angles

Tangent Function

Quadrants and Angle Measurement

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