All you have to do is memorize quadrant 1. If you memorize quadrant 1, then you can figure out the rest of the unit circle by reasoning through it.
So starting from the top, 90 degrees, and moving towards the right, down to 0 degrees, you will come across 3 angles, 60 degrees 45 degrees, and 30 degrees.
They follow a pattern: (√1/2, √3/2) (60 degrees) (√2/2, √2/2) (45 degrees) (√3/2, √1/2) (30 degrees)
Notice the 1,2,3 pattern and the 3,2,1 pattern. And that each of them is a fraction with a 2 in the denominator.
If you can memorize the above, then the rest of the unit circle is just those values, but they make be positive or negative depending on which quadrant you are in.
If you understand how the x-y coordinates work, then you should be able to figure out the positive or negative aspect of the unit circle.
For example, in quadrant 1, both x and y are positive. In quadrant 2, the x is negative and the y is positive. So if I wanted to know angle 150 degrees. I recognize it is going to be the same point as the 30 degrees which is (√3/2, √1/2). But since it is in quadrant 2, the x is negative. Thus for 150 degrees, the unit circle says (-√3/2, √1/2)
Another example, 315 degrees will have the same point as 45 degrees which is (√2/2, √2/2). But since it is in quadrant 4, the x is positive and the y is negative. Thus, the unit circle for 315 degrees is (√2/2, -√2/2)
You can do this using synthetic division, which is the easiest way. If x - 2 = 0, then x = 2. That 2 will go outside the "box" and the leading coefficients of the terms in the polynomial will go inside the "box". 2 (1 -3 -10 24). Bring down the first number, the 1. Multiply that 1 by the 2 to get 2. Put that 2 up under the -3 and add to get -1. Multiply that -1 by the 2 to get -2. Put that =-2 up under the -10 and add to get -12. Multiply that -12 by the 2 to get -24. Put the -24 up under the 24 and add to get 0. That means that x - 2 is a factor of the polynomial. What's left, the bolded numbers, are the coefficients of a new polynomial that is one degree less than the polynomial you started with. In other words, when we divide your polynomial by x-2, you get .