# Signs of Trigonometric Functions

• Angle (argument of a function): $$\alpha$$
Trigonometric functions: $$\sin \alpha,$$ $$\cos \alpha ,$$ $$\tan \alpha,$$ $$\cot \alpha,$$ $$\sec \alpha,$$ $$\csc \alpha$$
Coordinates of a point on a circle: $$x$$, $$y$$
1. Four quadrants of the unit circle
The trigonometric circle is divided into $$4$$ quarters (quadrants). The first quadrant corresponds to the angle interval $$0^\circ \lt \alpha \lt 90^\circ,$$ the second quadrant lies in the interval $$90^\circ \lt \alpha \lt 180^\circ,$$ the third quadrant corresponds to the interval $$180^\circ \lt \alpha \lt 270^\circ,$$ and the fourth quadrant covers the angles $$270^\circ \lt \alpha \lt 360^\circ.$$
2. The signs of the trigonometric functions depend on the quadrant in which the angle lies. The table below shows the signs of $$6$$ trigonometric functions in quadrants $$I-IV$$.
3. Signs of the trigonometric functions in the unit circle