Find each exact function value. See Example 2.
csc 11π/6...

Question

Find each exact function value. See Example 2.

csc 11π/6

Accepted Answer

Welcome back. I am so glad you're here. We are asked to determine the exact value of the given function. Our given function is the kant of seven pi divided by six. Our answer choices are answer choice, a negative square root three, answer choice B two, answer choice C negative two and answer choice D square root three. All right. We recall from previous lessons and from the figure of the unit circle in the textbook that seven pi divided by six is an angle on the unit circle. So I'm going to draw some of the unit circle, not the whole thing, but you can definitely refer to the unit circle figure in your textbook for more details. So we've got a vertical y axis and a horizontal X axis. They come together at the origin in the middle, the unit circle lies over that and every point on the unit circle is one unit away from the origin. And you can use your imagination that what I drew is a perfect circle. So for seven pi divided by six, the initial side is along the positive part of the X axis, then we head counter clockwise and we're gonna head all the way into the third quadrant. So down and to the left of the origin seven pi divided by six is equal to 210 degrees. And the X and Y coordinates that you can see from the figure of the unit circle in the textbook are the X coordinate is negative square root three divided by two and the Y coordinate is negative one half. Now, why is this significant? Well, we recall from previous lessons and from the textbook that the CC can't of any angle on the unit circle and we call that s is equal to one divided by Y. And so why here is negative one half, we take one divided by negative one half. Whenever there's a fraction within our fraction, I like to rewrite this with the division symbol. So one divided by negative one half because that reminds me to multiply by the reciprocal of the second fraction. So this is the same as one multiplied by negative two. It's negative two divided by one, but that's negative two and one multiplied by negative two is negative two. So the coast he can't of seven pi divided by six is exactly negative two. We look at our answer choices and this matches with answer choice. C well done. We'll catch you on the next one.

Find each exact function value. See Example 2.
csc 11π/6

Key Concepts

Cosecant Function

Unit Circle

Reference Angles

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