 So we do want to take off the training wheels and start talking about angles in radians. And the reason is that while practical trigonometry often measures angles in radians, every use of trigonometry in advanced mathematics uses radians. And in fact, after this course, you will never use degrees again. At least not in mathematics. Now, I know some of you are saying, oh, good riddance. But for those of you who are continuing to take mathematics, the reason that you'll never use degrees again will become apparent in calculus. Now, remember, if our angle is in standard position, the radian measure of an angle corresponds to the distance along the unit circle from the positive x-axis to the point where the terminal side of the angle meets the unit circle. And there are some important benchmarks. If we go all the way around, that's 2 pi radians. If we go halfway around, that's pi radians. And if we go one-quarter of the way around, that's pi over 2 radians. So let's try to find the exact value of sine, cosine, and tangent of pi over 6. And remember, you don't have to specify that we're using radian measure. So here, because we're given the angle pi over 6, and we're not told it's in degrees, we should assume that this is an angle in radians. Now, because we're used to degrees, we might begin by finding the corresponding angle in degrees, but you should eventually learn to think in radians. So we might start out with the following idea. A full turn is 360 degrees. That's the same as 2 pi radians. And since we want pi over 6 radians, we'll take one-twelfth of 2 pi. And so that gives us pi over 6 radians is the same as 30 degrees. So the sine, cosine, and tangent of pi over 6 radians is the same as the sine, cosine, and tangent of 30 degrees. Now, it's traditional to remember the exact values for sine and cosine of a number of angles, but if you don't remember them, here they are. And so we can read off our values of sine and cosine, and tangent, remember, is sine over cosine. Now, since we know the exact values of sine and cosine for angles of 0, 30 degrees, 45 degrees, 60 degrees, and 90 degrees, this means we can find the exact values of sine and cosine for angles of 0 radians, pi over 6 radians, pi over 4 radians, pi over 3 radians, and pi over 2 radians. And these are, and tangent you can figure out once you know the values of sine and cosine. What about the cosine of 7 pi over 6? So remember that pi is halfway around, so 7 pi over 6 is a little bit more than halfway around. We'll draw a picture, we'll do a little bit of arithmetic, and note that we have 7 pi over 6 is pi plus pi over 6, so our reference angle, this bit, is pi over 6. Now our table tells us that cosine of pi over 6 is square root of 3 over 2, so that's our x-coordinate, but since we're in the third quadrant, cosine of 7 pi over 6 will be the negative of this value, and so that gives us cosine of 7 pi over 6 equals negative square root of 3 over 2.