Unit Circle Radians

Unit Circle

What is Unit Circle?

It can be defined as a circle that has one unit of radius. Cartesian coordinates are commonly used to represent unit circles. With two variables x and y, we can algebraically represent the unit circle. Trigonometric ratios like sine, cosine, and tangent can be found with the unit circle in trigonometry.


If a circle has a radius of 1 then the circle is called a unit circle. 

Equation of a Unit Circle

A circle has the center (a, b) and the radius r, and its equation is [katex]\left(x-a\right)^2+\left(y-b\right)^2=r^2[/katex]. As a result of simplifying this equation, we can obtain an equation for a unit circle. The origin of the coordinate axes is at point (0, 0), so the center of the unit circle is there. 1 unit radius. Hence the unit circle has [katex]\left(x-0\right)^2+\left(y-0\right)^2=1^2[/katex].equation.

Unit Circle radian


 When the radius is taken, we make a certain angle

It should be wrapped around the circle.

1 Radian is about [katex] 57.2958[/katex]. degrees

π radians =180°

So 1 radian =180°/π


Radians are converted to degrees by multiplying by 180 and dividing by π

Degrees converted to radians, multiply by π, divide by 180

The degree unit is easy to understand by common people and the radian unit is used by mathematicians.

Unit Circle With Tangent

For standard angles from 0° to 360°, the unit circle with a tangent gives values of the tangent function (called tan). Sin (sine function) and cos (cosine function) are usually calculated from the general unit circle. Using[katex]tan x = (sin x)/(cos x)[/katex]., it is possible to compute the unit circle with tangent using tan, sin, and cos.


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