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.
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 = 0 0
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 0 0 = Opposite side / Hypotenuse = 0/1 = 0
cos 0 0 = Adjacent side / Hypotenuse = 1/1 = 1
tan 0 0 = Opposite side / Adjacent side = 0/1 = 0
2. For θ = 90 0
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 90 0 = Opposite side / Hypotenuse = 1/1 = 1
cos 90 0 = Adjacent side / Hypotenuse= 0/1 = 0
tan 90 0 = Opposite side / Adjacent side = 1/0 = Not defined
3. For θ = 180 0
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 180 0 = Opposite side / Hypotenuse = 0/1 = 0
cos 180 0 = Adjacent side / Hypotenuse= 0-1/1 = -1
tan 180 0 = Opposite side / Adjacent side = 0/-1 = 0
4. For θ = 270 0
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 270 0 = Opposite side / Hypotenuse = -1/1 = -1
cos 270 0 = Adjacent side / Hypotenuse= 0/-1 = 0
tan 270 0 = Opposite side / Adjacent side = -1/0 = Not defined
A quadrantal angle is an angle in the standard position and has a measure which is a multiple of 90 0 or π/2 radians. It is an angle in a standard position whose terminal ray lies along one of the axes.
sin 0 0 = 0
cos 0 0 = 1
tan 0 0 = 0
sin 90 0 = 1
cos 90 0 = 0
tan 90 0 = Not defined