Solved Examples on Unit Circle
Q1: Prove that point Q lies on a unit circle, Q = [1/√(6), √4/√6]
Solution:
Given,
- Q = [1/√(6), √4/√6]
x = 1/√(6), y = √4/√6
Equation of Unit Circle is,
x2 + y2 = 1
LHS = (1/√(6))2 + (√4/√6)2
LHS = 1/6 + 4/6 = 5/6 ≠ 1
LHS ≠ RHS
Thus, point Q[1/√(6), √4/√6] does not lie on the unit circle.
Q2: Compute tan 30o using the sin and cos values of the unit circle.
Solution:
tan 30° using sin and cos values,
tan 30° = (sin 30°)/ (cos 30°)
- sin 30° = 1/2
- cos 30° = √(3)/2
tan 30° = 1/2/√(3)/2
tan 30° = 1/√(3)
Q3: Validate if the point P [1/2, √(3)/2] lies on the unit circle.
Solution:
Given,
P = [1/2, √(3)/2]
- x = 1/2
- y = √(3)/2
Equation of Unit Circle is,
- x2 + y2 = 1
LHS
= (1/2)2 + (√(3)/2)2
= 1/4 + 3/4
= (1 + 3)/4 = 4/4
= 1
= RHS
Unit Circle: Definition, Formula, Diagram and Solved Examples
Unit Circle is a Circle whose radius is 1. The center of unit circle is at origin(0,0) on the axis. The circumference of Unit Circle is 2π units, whereas area of Unit Circle is π units2. It carries all the properties of Circle. Unit Circle has the equation x2 + y2 = 1. This Unit Circle helps in defining various Trigonometric concepts.
The Unit Circle is often denoted as S1 generalization to higher dimensions is the unit sphere. Let’s understand more about Unit Circle, Formula and Solved examples in detail below.