**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.

**Definition**

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**

**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**

**=57.2958…°(approximately) **

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.

Degrees | Radians | tan |

[katex]0°[/katex] | [katex]0[/katex] | [katex]0[/katex] |

[katex]30°[/katex] | [katex]\pi/6[/katex] | [katex]\sqrt3/3[/katex] |

[katex]45°[/katex] | [katex]\pi/4[/katex] | [katex]1[/katex] |

[katex]60°[/katex] | [katex]\pi/3[/katex] | [katex]\sqrt3[/katex] |

[katex]90°[/katex] | [katex]\pi/2[/katex] | [katex]undefined[/katex] |

[katex]120°[/katex] | [katex]2\pi/3[/katex] | [katex]-\sqrt3[/katex] |

[katex]135°[/katex] | [katex]3\pi/4[/katex] | [katex]-1[/katex] |

[katex]150°[/katex] | [katex]5\pi/6[/katex] | [katex]-\sqrt3/3[/katex] |

[katex]180°[/katex] | [katex]\pi[/katex] | [katex]0[/katex] |

[katex]210°[/katex] | [katex]7\pi/6[/katex] | [katex]\sqrt3/3[/katex] |

[katex]225°[/katex] | [katex]5\pi/4[/katex] | [katex]1[/katex] |

[katex]240°[/katex] | [katex]4\pi/3[/katex] | [katex]\sqrt3[/katex] |

[katex]270°[/katex] | [katex]3\pi/2[/katex] | [katex]undefined[/katex] |

[katex]300°[/katex] | [katex]5\pi/3[/katex] | [katex]-\sqrt3[/katex] |

[katex]315°[/katex] | [katex]7\pi/4[/katex] | [katex]-1[/katex] |

[katex]330°[/katex] | [katex]11\pi/6[/katex] | [katex]-\sqrt3/3[/katex] |

[katex]360°[/katex] | [katex]2\pi[/katex] | [katex]0[/katex] |