**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 \left(x-a\right)^2+\left(y-b\right)^2=r^2. 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 \left(x-0\right)^2+\left(y-0\right)^2=1^2.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* 57.2958. 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. Usingtan x = (sin x)/(cos x)., it is possible to compute the unit circle with tangent using tan, sin, and cos.

Degrees | Radians | tan |

0° | 0 | 0 |

30° | \pi/6 | \sqrt3/3 |

45° | \pi/4 | 1 |

60° | \pi/3 | \sqrt3 |

90° | \pi/2 | undefined |

120° | 2\pi/3 | -\sqrt3 |

135° | 3\pi/4 | -1 |

150° | 5\pi/6 | -\sqrt3/3 |

180° | \pi | 0 |

210° | 7\pi/6 | \sqrt3/3 |

225° | 5\pi/4 | 1 |

240° | 4\pi/3 | \sqrt3 |

270° | 3\pi/2 | undefined |

300° | 5\pi/3 | -\sqrt3 |

315° | 7\pi/4 | -1 |

330° | 11\pi/6 | -\sqrt3/3 |

360° | 2\pi | 0 |