Trigonometry is a branch in mathematics, which involves the study of relationship involving the length and angles of a triangle. It is generally associated with a right-angled triangle, where one of the angles is always 90 degrees.

It has a wide number of application in other fields of mathematics. Well, the use of trigonometry is used to map with the help of a triangle. Interestingly, it is said that Ancient Greeks were used to trigonometry to calculate the distance from the Earth to the Moon.

All these calculations can be easily figured out using the tables of trigonometric functions. The trigonometric table is useful in the number of areas. Trigonometry Table is essential for navigation, science, and engineering. The trigonometric table was effectively used in the pre-digital era, even before the existence of pocket calculators. Further, the trigonometric table led to the development of the first mechanical computing devices.

The Trigonometrical ratios table helps to find the values of trigonometric standard angles such as 0°, 30°, 45°, 60° and 90°. The values of trigonometrical ratios of standard angles are very important to solve the trigonometrical problems. Therefore, it is necessary to remember the value of the trigonometrical ratios of these standard angles. Another important application of trigonometric tables is for Fast Fourier Transform (FFT) algorithms.

The trigonometric table consists of trigonometric ratios – sine, cosine, tangent, cosecant, secant, cotangent. These ratios can be written in short as sin, cos, tan, cosec, sec and cot.

Trigonometry Ratio Table |
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Angles (In Degrees) |
\(0^{\circ }\) | \(30^{\circ }\) | \(45^{\circ }\) | \(60^{\circ }\) | \(90^{\circ }\) | \(180^{\circ }\) | \(270^{\circ }\) | \(360^{\circ }\) |

Angles (In Radians) |
\(0\) | \(\large \frac{\pi}{6}\) | \(\large\frac{\pi}{4}\) | \(\large\frac{\pi}{3}\) | \(\large\frac{\pi}{2}\) | \(\large\large\pi\) | \(\large\frac{3\pi }{2}\) | \(2\pi\) |

\(\sin\) | \(0\) | \(\large\frac{1}{2}\) | \(\large \frac{1}{\sqrt{2}}\) | \(\large\frac{\sqrt{3}}{2}\) | \(1\) | \(0\) | \(-1\) | \(0\) |

\(\cos\) | \(1\) | \(\large\frac{\sqrt{3}}{2}\) | \(\large\frac{1}{\sqrt{2}}\) | \(\large\frac{1}{2}\) | \(0\) | \(-1\) | \(0\) | \(1\) |

\(\tan\) | \(0\) | \(\large\frac{1}{\sqrt{3}}\) | \(1\) | \(\large\sqrt{3}\) | Not Defined | \(0\) | Not Defined | \(1\) |

\(\cot\) | Not Defined | \(\large\sqrt{3}\) | \(1\) | \(\large\frac{1}{\sqrt{3}}\) | \(0\) | Not Defined | \(0\) | Not Defined |

\(\csc\) | Not Defined | \(2\) | \(\large\sqrt{2}\) | \(\large\frac{2}{\sqrt{3}}\) | \(1\) | Not Defined | \(-1\) | Not Defined |

\(\sec\) | \(1\) | \(\large\frac{2}{\sqrt{3}}\) | \(\large\sqrt{2}\) | \(2\) | Not Defined | \(-1\) | Not Defined | \(1\) |

**How To Remember Trigonometry Table In Easy Way?**

Remembering the trigonometry table will help in many ways, and it is easy to remember the table. If you know the trigonometry formulas than remembering the trigonometry table is very easy. The Trigonometry ratio table id depended upon the trigonometry formulas in the similar way all the functions of trigonometry are depended on each aspect and interlinked with each other.

Below are the few steps to memorize the trigonometry table.

Before beginning try to remember these values, recall and remember below trigonometry formulas.

\(\sin x = \cos (90^{\circ}-x)\)

\(\cos x=\sin (90^{\circ}-x)\)

\(\tan x = \cot (90^{\circ}-x)\)

\(\cot x = \tan (90^{\circ}-x)\)

\(\sec x = \cot (90^{\circ}-x)\)

\(\cot x = \sec (90^{\circ}-x)\)

\(\large \frac{1}{\sin\:x}=\frac{1}{\cos\:x}=\) \(\sin\:x\)

\(\frac{1}{\cos\:x}=\) \(\sec\:x\)

\(\frac{1}{\sec\:x}=\) \(\cos\:x\)

\(\frac{1}{\tan\:x}=\) \(\cot\:x\)

\(\frac{1}{\cot\:x}=\) \(\tan\:x\)

**Steps to Create Trigonometry Table:**

**Step 1: **

Create a table with the top row listing the angles such as 0, 30, 45, 60, 90, and write all trigonometric function in first column such as sin, cos, tan, cosec, sec, cot.

**Step 2: Determine the value of sin. **

To determine the value of sin divide all the value by 4 with all root. See the example below.

To determine the value of \(\sin 0^{\circ}\)

\(\sqrt{\frac{0}{4}}=0\)

In a similar way, dividing all the angles with the value of sin. The answer would be.

Angles (In Degrees) | \(0^{\circ }\) | \(30^{\circ }\) | \(45^{\circ }\) | \(60^{\circ }\) | \(90^{\circ }\) | \(180^{\circ }\) | \(270^{\circ }\) | \(360^{\circ }\) |

\(\sin\) | \(0\) | \(\frac{1}{2}\) | \(\frac{1}{\sqrt{2}}\) | \(\frac{\sqrt{3}}{2}\) | \(1\) | \(0\) | \(-1\) | \(0\) |

**Step 3: Determine the value of cos.**

The cos-value is opposite angle of sin angle it means which value of sin on 0-degree angle the same value is cos on 90-degree angle. To determine the value of cos divide by 4 in opposite sequence of sin. For this divide of 4 by 4 with all root such as. See the example below.

To determine the value of \(\cos 0^{\circ}\)

\(\sqrt{\frac{4}{4}}=1\)

In a similar way, dividing all the angles with the value of cos. The answer would be.

Angles (In Degrees) | \(0^{\circ }\) | \(30^{\circ }\) | \(45^{\circ }\) | \(60^{\circ }\) | \(90^{\circ }\) | \(180^{\circ }\) | \(270^{\circ }\) | \(360^{\circ }\) |

\(\cos\) | \(1\) | \(\frac{\sqrt{3}}{2}\) | \(\frac{1}{\sqrt{2}}\) | \(\frac{1}{2}\) | \(0\) | \(-1\) | \(0\) | \(1\) |

**Step 4: Determine the value of tan.**

The tan is equal to sin divided by cos. \(\tan = \frac{\sin}{\cos}\). To determine the value of tan on \(0^{\circ }\) divide the value of sin on \(0^{\circ }\) by the value of cos on \(0^{\circ }\). See example below.

\(\tan 0^{\circ }=\frac{0}{1}=0\)

In similar way, the table would be.

Angles (In Degrees) | \(0^{\circ }\) | \(30^{\circ }\) | \(45^{\circ }\) | \(60^{\circ }\) | \(90^{\circ }\) | \(180^{\circ }\) | \(270^{\circ }\) | \(360^{\circ }\) |

\(\tan\) | \(0\) | \(\frac{1}{\sqrt{3}}\) | \(1\) | \(\sqrt{3}\) | Not Defined | \(0\) | Not Defined | \(1\) |

**Step 5: Determine the value of cot.**

The value of cot can be determined by all opposite value of tan. The value of tan on \(0^{\circ }\) is the opposite of tan on \(0^{\circ }\). So the value will be:

\(\cot 0^{\circ }=\frac{1}{0}=Infinite \; or\; Not\; Defined\)

Same way, the table for a sec is below.

Angles (In Degrees) | \(0^{\circ }\) | \(30^{\circ }\) | \(45^{\circ }\) | \(60^{\circ }\) | \(90^{\circ }\) | \(180^{\circ }\) | \(270^{\circ }\) | \(360^{\circ }\) |

\(\cot\) | Not Defined | \(\sqrt{3}\) | \(1\) | \(\frac{1}{\sqrt{3}}\) | \(0\) | Not Defined | \(0\) | Not Defined |

**Step 6: Determine the value of cosec.**

The value of cosec on \(0^{\circ }\) is the opposite of sin on \(0^{\circ }\).

\(\csc 0^{\circ }=\frac{1}{0}=Infinitive\; or\; Not\; Defined\)

Same way, the table for cosec is below.

Angles (In Degrees) | \(0^{\circ }\) | \(30^{\circ }\) | \(45^{\circ }\) | \(60^{\circ }\) | \(90^{\circ }\) | \(180^{\circ }\) | \(270^{\circ }\) | \(360^{\circ }\) |

\(\csc\) | Not Defined | \(2\) | \(\sqrt{2}\) | \(\frac{2}{\sqrt{3}}\) | \(1\) | Not Defined | \(-1\) | Not Defined |

**Step 7: Determine the value of sec.**

The value of sec can be determined by all opposite value of cos. The value of sec on \(0^{\circ }\) is the opposite of cos on \(0^{\circ }\). So the value will be:

\(\sec 0^{\circ }=\frac{1}{1}=1\)

Same way, the table for sec is below.

Angles (In Degrees) | \(0^{\circ }\) | \(30^{\circ }\) | \(45^{\circ }\) | \(60^{\circ }\) | \(90^{\circ }\) | \(180^{\circ }\) | \(270^{\circ }\) | \(360^{\circ }\) |

\(\sec\) | \(1\) | \(\frac{2}{\sqrt{3}}\) | \(\sqrt{2}\) | \(2\) | Not Defined | \(-1\) | Not Defined | \(1\) |