Formulas and Tables

Trigonometry

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 \(270^\circ \lt \alpha \lt 360^\circ.\)
Four quadrants of the unit circle
  1. 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 \(I-IV\).
Signs of the trigonometric functions
  1. Signs of the trigonometric functions in the unit circle
Signs of the sine and cosecant functions
Signs of the cosine and secant functions
Signs of the tangent and cotangent functions