Unit Circle with Sin Cos and Tan
Any point on the unit circle with the coordinates (x, y), is represented using trigonometric identies as, (cosθ, sinθ). The coordinates of the radius corners represent the cosine and the sine of the θ values for a particular value of θ and the radius line. We have cos θ = x, and sin θ = y. There are four parts of a circle each lying in one quadrant, making an angle of 90°,180°, 270°, and 360°. The radius values lie between -1 to 1 respectively. Also, the sin θ and cos θ values lie between 1 and -1 respectively.
Unit Circle and Trigonometric Identities
The unit circle trigonometric identities for cotangent, secant, and cosecant can be computed using the identities for sin, cos, and tan. Conclusively, we obtain a right-angled triangle with the sides 1, x, and y respectively. Computing the unit circle identities can be expressed as,
- sin θ = y/1
- cos θ = x/1
- tan θ = y/x
- sec θ = 1/x
- cosec θ = 1/y
- cot θ = x/y
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.