Definitions and notable values

Definition

Let t be a real number and M the point on the unit circle associated with t by winding. By definition:

• cos(t) is the abscissa (x-coordinate) of point M
• sin(t) is the ordinate (y-coordinate) of point M

Thus, for any real number t, M has coordinates (cos(t), sin(t)).

Important values to know by heart

t	0	π/6	π/4	π/3	π/2
cos(t)	1	√3/2	√2/2	1/2	0
sin(t)	0	1/2	√2/2	√3/2	1

Mnemonic: the numerators under the square root follow 0, 1, 2, 3, 4 (√0, √1, √2, √3, sqrt(4), all divided by 2) for the sine in ascending order of t, and in reverse order for the cosine.

Example of use

For t = pi/4 (45 degrees), we have cos(pi/4) = sin(pi/4) = sqrt(2)/2, which corresponds to the point on the circle situated exactly on the first bisector.

Common pitfall

Do not confuse cos(pi/6) and sin(pi/6): the cosine of pi/6 is sqrt(3)/2 (not 1/2), and it is the sine of pi/6 that is 1/2. The table above is symmetrical about pi/4, which helps you to remember both rows without mixing them up.