The unit circle has been divided into twelve equal arcs, corresponding to t-values of

0, 𝜋/6, 𝜋/3, 𝜋/2, 2𝜋/3, 5𝜋/6, 𝜋, 7𝜋/6, 4𝜋/3, 3𝜋/2, 5𝜋/3, 11𝜋/6, and 2𝜋

Use the (x,y) coordinates in the figure to find the value of each trigonometric function at the indicated real number, t, or state that the expression is undefined.

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sin 3𝜋/2

Video transcript

Welcome back everyone. In this problem, the circle with a radius of one unit is partitioned into 12 equal arcs where each arc corresponds to specific values determine the value of each trigonometric function at the given real number using the coordinates in the diagram or specify that the expression is undefined. We're trying to figure out the value for the sign of 1/6 of pi. And for our answer choices A says that it's route three divided by two B says it's a half C negative root two divided by two and D says it's undefined. Now, what do we know about our unit circle that can help us evaluate the trigonometric function? Well, recall OK. That in the unit circle in the unit circa? OK. Then for each coordinate, the X value is equal to CT and the Y value is equal to sine T. OK. So that's what we know about the coordinates. So here in our problem for the sine of 1/6 of pi, OK, then T equals 1/6 of pi. So at T equals a 1/6 of pi, what do we know about the X and Y coordinates? Well, if we go to our unit circle here and go to a six stuff pie. Notice that the coordinates are going to be root three divided by 2.5. Since we know that X equals CT and Y equals sine T, that must mean then OK, that the sine of T, in this case, 1/6 of pi is the Y coordinate or a half. Therefore, when we go back to our answer choices, that means that B is the correct answer. Thanks a lot for watching everyone. I hope this video helped.