Find each exact function value. See Example 2. sin 7π/6

Video transcript

Welcome back. I am so glad you're here. We're asked to determine the exact value of the given function. Our given function is the sign of 11 pi divided by six. Our answer choices are answer choice, a negative square root three divided by two, answer choice B one half, answer choice C negative one half and answer choice D square root three divided by two. All right. So we've got this angle of 11 pi divided by six radiant. And we recall from previous lessons and from the unit circle in the textbook that 11 pi divided by six is an angle on our unit circle. I'm going to draw some of the unit circle, not all of it, but be sure to reference the one in your textbook, we've got a vertical Y axis and a horizontal X axis. They come together at the origin in the middle. And then the unit circle overlays that every part of the unit circle is one degree away from the origin. So you or not one degree one unit. And you can imagine that I've drawn a perfect circle here. So for the angle 11 pi divided by six, if our initial side is along the positive part of the X axis. We're going to head counterclockwise 11 pi divided by six radians, which is all the way in the fourth quadrant. So down into the right of the origin, 11 pie divided by six radians is the same as 330 degrees. And the X and Y values at 11 pi divided by six are square at three divided by two. That's the X value and negative one half is our Y value. So why is all of this significant? Well, we recall from previous lessons and from the textbook that the sign of an angle on our unit circle S is equal to the Y value. So here, the sign of 11 pi divided by six is equal to the Y value at 11 pi divided by six. The Y value here is negative one half. So the sign of 11 pi divided by six is negative one half. And that's that we look at our answer choices and this matches with answer choice. C well done. We'll catch you on the next one.