# Trig Degree Calculator

Welcome to this trig degree calculator, a tool created to calculate trigonometric functions instantly, so you don't have to use those boring trig degree charts.

To use this trig degree calculator:

**Input the angle, and the calculator will display the six trig functions**evaluated at such an angle.- You can use the
**radian**or the**degree mode**for this trig calculator, so you're not limited to inputting the angle in degrees.

## Trigonometric functions

A **trigonometric function** is a function that takes an **angle** as its argument. One of the applications of trigonometric functions is analyzing right triangles by relating their sides' lengths to their angles. In our right triangle trigonometry calculator, you can see how we do it.

Although right triangles are limited to acute angles (apart from the right one), **we can evaluate these functions at any angle** (see our trigonometric functions calculator). In the following section, you can look at a chart of values of trigonometric functions evaluated at the most common angles.

## Trig degree chart (with fractions and decimals)

#### Trig degree chart with fractions and square roots

Angle (θ) | sin(θ) | cos(θ) | tan(θ) | cot(θ) | sec(θ) | csc(θ) |
---|---|---|---|---|---|---|

0° | 0 | 1 | 0 | und | 1 | und |

30° | 1/2 | (√3)/2 | 1/√3 | √3 | 2/√3 | 2 |

45° | 1/√2 | 1/√2 | 1 | 1 | √2 | √2 |

60° | (√3)/2 | 1/2 | √3 | 1/√3 | 2 | 2/√3 |

90° | 1 | 0 | und | 0 | und | 1 |

120° | (√3)/2 | -1/2 | -√3 | -1/√3 | -2 | 2/√3 |

135° | 1/√2 | -1/√2 | -1 | -1 | -√2 | √2 |

150° | 1/2 | -(√3)/2 | -1/√3 | -√3 | -2/√3 | 2 |

180° | 0 | -1 | 0 | und | -1 | und |

210° | -1/2 | -(√3)/2 | 1/√3 | √3 | -2/√3 | -2 |

225° | -1/√2 | -1/√2 | 1 | 1 | -√2 | -√2 |

240° | -(√3)/2 | -1/2 | √3 | 1/√3 | -2 | -2/√3 |

270° | -1 | 0 | und | 0 | und | -1 |

300° | -(√3)/2 | 1/2 | -√3 | -1/√3 | 2 | -2/√3 |

315° | -1/√2 | 1/√2 | -1 | -1 | √2 | -√2 |

330° | -1/2 | (√3)/2 | -1/√3 | -√3 | 2/√3 | -2 |

360° | 0 | 1 | 0 | und | 1 | und |

#### Trig degree chart with decimals

Angle (θ) | sin(θ) | cos(θ) | tan(θ) | cot(θ) | sec(θ) | csc(θ) |
---|---|---|---|---|---|---|

0° | 0 | 1 | 0 | und | 1 | und |

30° | 0.5 | 0.8660254 | 0.57735027 | 1.73205081 | 1.15470054 | 2 |

45° | 0.70710678 | 0.70710678 | 1 | 1 | 1.41421356 | 1.41421356 |

60° | 0.8660254 | 0.5 | 1.73205081 | 0.57735027 | 2 | 1.15470054 |

90° | 1 | 0 | und | 0 | und | 1 |

120° | 0.8660254 | -0.5 | -1.73205081 | -0.57735027 | -2 | 1.15470054 |

135° | 0.70710678 | -0.70710678 | -1 | -1 | -1.41421356 | 1.41421356 |

150° | 0.5 | -0.8660254 | -0.57735027 | -1.73205081 | -1.15470054 | 2 |

180° | 0 | -1 | 0 | und | -1 | und |

210° | -0.5 | -0.8660254 | 0.57735027 | 1.73205081 | -1.15470054 | -2 |

225° | -0.70710678 | -0.70710678 | 1 | 1 | -1.41421356 | -1.41421356 |

240° | -0.8660254 | -0.5 | 1.73205081 | 0.57735027 | -2 | -1.15470054 |

270° | -1 | 0 | und | 0 | und | -1 |

300° | -0.8660254 | 0.5 | -1.73205081 | -0.57735027 | 2 | -1.15470054 |

315° | -0.70710678 | 0.70710678 | -1 | -1 | 1.41421356 | -1.41421356 |

330° | -0.5 | 0.8660254 | -0.57735027 | -1.73205081 | 1.15470054 | -2 |

360° | 0 | 1 | 0 | und | 1 | und |

## Important comments about the trig degree charts

- The
**first table**provides the values using fractions and square roots, which minimize the loss of precision in problems in which we're performing many calculations. Apart from that, they are more compact and easier to write. - The
**second table**is the same as the first one but with decimals, which can help you compare different values. - Initially, we only need the sine and cosine values, and then can deduct the remaining functions by using the following trigonometric identities:
**tan(**;*θ*) = sin(*θ*)/cos(*θ*)- e.g. tan(30°) = sin(30°)/cos(30°) = (1/2)/(√3/2) = 1/√3

**cot(***θ*) = cos(*θ*)/sin(*θ*)- e.g. cot(30°) = cos(30°)/sin(30°) = (√3/2)/(1/2) = √3

**sec(***θ*) = 1/cos(*θ*)- e.g. sec(30°) = 1/cos(30°) = 1/(√3/2) = 2/√3

**csc(***θ*) = 1/sin(*θ*)- e.g. csc(30°) = 1/sin(30°) = 1/(1/2) = 2

**und**stands for**undefined values**, which, in this case, correspond to functions that require**dividing by zero**(something that doesn't have a mathematical definition). For example, as tan(90°) = sin(90°)/cos(90°) = 1/0, the tangent of 90 degrees is undefined.

## Other radian and degree mode trig calculators

## FAQ

### What are the values of the 6 trig functions for 330 degrees?

The values of the 6 trig functions for 330 degrees are:

- sin(330°) = -0.5;
- cos(330°) = √3/2 ≈ 0.8660254;
- tan(330°)= -1/√3 = -√3/3 ≈ -0.57735027 ;
- cot(330°) = -√3 ≈ -1.73205081;
- sec(330°) = 2/√3 ≈ 1.15470054; and
- csc(330°) = -2.

### How do I find the value of the 6 trig functions of 330 degrees?

To calculate the trig functions at 330 degrees:

- Use our trig degree calculator to obtain the values of sin(330°) and cos(330°):
- sin(330°) = 1/2;
- cos(330°) = √3/2;

- With the previous two results and some trig identities, obtain the other functions:
- tan(330°) = sin(330°)/cos(330°) = (1/2)/(√3/2) = 1/√3;
- cot(330°) = cos(330°)/sin(330°) = (√3/2)/(1/2) = √3;
- sec(330°) = 1/cos(330°) = 1/(√3/2) = 2/√3;
- csc(330°) = 1/sin(330°) = 1/(1/2) = 2.

### What trig functions are negative in which quadrants?

The trig functions of the trigonometric unit circle are negative at the following quadrants

**Quadrant I:**there's no negative function;**Quadrant II:**cosine, tangent, cotantent, and secant are negatives;**Quadrant III:**sine, cosine, secant and cosecant are negatives; and**Quadrant IV:**sine, tangent, cotangent, and cosecant are negatives.