Trigonometry is a branch in mathematics that studies length, angles and the relationship of the same with triangles. The practical application of trigonometry like the calculation of geometric values and heights makes understanding trigonometric values important. A __ trigonometric table__ serves as a collection consisting of values of different trigonometric angles like 0°, 30°, 45°, 60°, and 90°. One can locate the values of trigonometric ratios of sine, cosine, tangent, cosec, sec and cot. The trigonometry table serves as a collection of all the values of which one can refer to without any need for memorizing the same. The value of a trigonometric table can be used for various purposes like in science and engineering. The steps for creating a trigonometric table are listed below which can prove to be of great benefit:

1. Creation of a table with one row dedicated to angles like 0°, 30°, 45°, 60° and 90°. Dedicated trigonometric functions are listed in a separate column which are sine, cosine, tangent, sec, cosecant and cot. The first step is easy and involves writing the basic information i.e trigonometric angles and functions.

2. Identification of different values:

To identify the value of sine trigonometric function, One is required to calculate the root of 0,1,2,3,4 divided by 4. For example, 0/4 is 0 and its root is 0. Therefore, sin 0° – 0. Similarly, 4/4 = 1 and its root is 1 therefore the value of sin 90° – 1.

The value of cos can be easily calculated by reversing the sequence of denominator values as used in sin i.e value of trigonometric functions from 0°- 90° for cos can be calculated by dividing 4,3,2,1 and 0 with 4 and calculating the root of the same. Therefore, the value of cos 90° is 0 and cos 60° is 1/2.

The value of Tan function can be calculated by dividing the value of sin and cos. For example, the value of tan 0° is 0 as the value of sin0° is 0 and cos 0° is 1.

The value of sec, cosec and cot can be easily calculated through the reciprocal of sin, cosine and cot. For example, the value of cosec 30° is 2 and sec 0° is 1.

A __ unit circle__ refers to a circle with a radius of 1. Unit circle can also be used for calculating trigonometric function values. Plotting a unit circle on a cartesian plane with the value of centre being (0,0). Also, the Equation of a Unit Circle: x2 + y2 = 1. This further can be used for calculating the values of different trigonometric functions.

1. Create a right-angled triangle with its hypotenuse as its radius. x and y being the value of lengths of base and altitude to the triangle. Therefore, (x,y) is the coordinate on the unit circle. The values of sine, cos and tan can be easily calculated through the use of the above values.

Trigonometrical ratio sine = altitude/hypotenuse which is equal to y/1 and cos = base/hypotenuse which is equal to x/1.

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