What do you mean by quadrantal angles? Angles in the standard position where the terminal side lies on the x-axis or y-axis are called quadrantal angles. These are measured in 90° increment, such as 90°, 180°, 270°, 360° and so on. In trigonometric ratios, we learnt trigonometric ratios for acute angles as the ratio of sides of a right-angled triangle. Here, we extend the definition of trigonometric ratios to any angle in terms of radian measure and study them as trigonometric functions. In this article, we will discuss how to find the trigonometric functions of quadrantal angles.

How to Find Trigonometry Functions of Quadrantal Angles

The angles which are integral multiples of π/2 are called quadrantal angles.

The trigonometric ratios of quadrantal angles are given below.

1. For θ = 0⁰

A point (x, y) = (1, 0) lies on the terminal side of the angle θ.

Here, x = 1 and y = 0

i.e., adjacent side = 1

Opposite side = 0

By Pythagoras’ theorem, we get the hypotenuse = 1

sin 0⁰ = Opposite side / Hypotenuse = 0/1 = 0

cos 0⁰ = Adjacent side / Hypotenuse = 1/1 = 1

tan 0⁰ = Opposite side / Adjacent side = 0/1 = 0

2. For θ = 90⁰

A point (x, y) = (0, 1) lies on the terminal side of angle θ.

Here, x = 0 and y = 1.

i.e., adjacent side = 0

Opposite side = 1

By Pythagoras’ theorem, we get the hypotenuse = 1

sin 90⁰ = Opposite side / Hypotenuse = 1/1 = 1

cos 90⁰ = Adjacent side / Hypotenuse= 0/1 = 0

tan 90⁰ = Opposite side / Adjacent side = 1/0 = Not defined

3. For θ = 180⁰

A point (x, y) = (-1, 0) lies on the terminal side of angle θ.

Here, x = -1 and y = 0.

i.e., adjacent side = -1

Opposite side = 0

By Pythagoras’ theorem, we get the hypotenuse = 1

sin 180⁰ = Opposite side / Hypotenuse = 0/1 = 0

cos 180⁰ = Adjacent side / Hypotenuse= 0-1/1 = -1

tan 180⁰ = Opposite side / Adjacent side = 0/-1 = 0

4. For θ = 270⁰

A point (x, y) = (0, -1) lies on the terminal side of angle θ.

Here, x = 0 and y = -1

i.e., adjacent side = 0

opposite side = -1

By Pythagoras’ theorem, we get the hypotenuse = 1

sin 270⁰ = Opposite side / Hypotenuse = -1/1 = -1

cos 270⁰ = Adjacent side / Hypotenuse= 0/-1 = 0

tan 270⁰ = Opposite side / Adjacent side = -1/0 = Not defined