 So if we have one trigonometric function, we could have compositions of trigonometric functions. For example, let's try to find the arc sign of 225 degrees. So by definition, arc sign of sine of 225 degrees is the angle theta, where the sine of theta is the same as the sine of 225 degrees, and theta is in the first or fourth quadrant. So first, let's draw an angle of 225 degrees in standard position. This angle meets the circle at some point x, y, where the sine of 225 degrees is equal to y. However, this angle is not in the first or fourth quadrant. And so we need to find an angle theta, where sine of theta equals y, and theta is in the first or fourth quadrant. So the thing to notice here is that while the angle of 225 degrees intersects the circle at b, where y is equal to sine of 225 degrees, there is another point b prime on the circle with the same y value. And it's right here. Now it's useful to keep in mind that the reference angle for 225 degrees is 45 degrees. So we can rotate clockwise from the positive x axis by 45 degrees to get to b prime. Since we need to rotate clockwise from the positive x axis to get to the terminal side of this angle, then theta is minus 45 degrees. And so that says a fourth quadrant angle theta, where sine of theta is the same as sine of 225 degrees, is theta equals minus 45 degrees, and so the arc sine of the sine of 225 degrees is minus 45 degrees. Or say we want to find the cosine of the arc sine of minus one-third. So remember the arc sine of minus one-third will be the first or fourth quadrant angle whose sine is minus one-third. On the unit circle, the sine is the y-coordinate. So we want to find the point b on the circle in the first or fourth quadrant, where y is equal to minus one-third. And this point is right here in the fourth quadrant. Since the point is on the unit circle x squared plus y squared equals one, and we know y equals minus one-third, we can also find x. Now the equation has two solutions plus or minus square root of eight-ninths. But since the point is in the fourth quadrant, we know that x has to be the positive solution square root of eight over nine. This gives us the coordinates of the point square root of eight over nine minus one-third. And remember, if it's not written down, it didn't happen. Let's write down the coordinates of the point. Now since the angle theta, which is the same as arc sine of minus one-third, goes through the point square root eight-ninths minus one-third on the unit circle, that means the cosine of theta is square root of eight-ninths.