Fig. 1a - Sine and cosine of the angle θ in the unit circle of a cartesian coordinate system.
In a Cartesian coordinate system, consider the unit circle, which is of radius 1 and centered at the origin (see Figure 1a). The ray (blue) forming angleθ with the positive x-axis intersects the unit circle at a point whose x-coordinate (red) is the cosine and whose y-coordinate (green) is the sine of θ. This defines and for all angles between 0 and 360°. Sine and cosine of θ are real numbers between -1 and +1.
Fig. 1b - Angle θ in the second quadrant. The sine is positive, the cosine negative.
Fig. 1c - Angle θ in the third quadrant. Both sine and cosine are negative.
Fig. 1d - Angle θ in the fourth quadrant. The sine is negative, the cosine positive.