As a result, sine will be positive, but cosine will be negative, and all tangent values will be negative.) In the third quadrant, all x and y values will be negative, so all sine and cosine values will be negative.
Then I think of a point in the second quadrant (x will be negative, since all the values for x will be less than zero, and y will be positive. The way I remind myself of these formulas is to think of a point in the first quadrant (both x and y will be positive, so all sine and cosine values will be positive, as will tangent). One way is to memorize the signs for the different trig functions in the four quadrants. There are ways of reconstructing the information if you forget. In the case of the symmetry relationships, it is a great time-saver to know these. Sometimes it is just plain easier to memorize a couple of formulas than to try to dig back to the basics and reconstruct the formulas.
No, you can get through a lot of math without memorizing, but it just takes a lot longer to do the problems.
