Trigonometric table

A trigonometric table is a table of values of trigonometric ratio like sin, cos, tan, cot, cosec and sec from 0 to 360. This trig table holds corners in degrees and radians, that very helpful for translation of degrees in radians or vice versa.

Trigonometric Values Table

You can see below the trigonometric values table or trigonometric table

Steps to create Trignomatic Table:

Creating a trigonometry table by hand involves using basic geometric principles and properties of special angles. Here’s how you can do it:

Step 1: Understand Special Triangles

30°-60°-90° Triangle

In a 30°-60°-90° triangle, the sides have a specific ratio:

• • The side opposite the 30° angle is \(\frac{1}{2} \)(half the hypotenuse).
  • The side opposite the 60° angle is \(\frac{√3}{2} \) (half the hypotenuse times √3 ).
  • The hypotenuse is 1.

45°-45°-90° Triangle

• In a 45°-45°-90° triangle, the sides have a specific ratio:
  • The sides opposite the 45° angles are both \(\frac{\sqrt{2}}{2}\) (half the hypotenuse times √2).
  • The hypotenuse is 1.

Step 2: Use the Unit Circle

• For angles not covered by special triangles, the unit circle is a powerful tool. The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane.

Step 3: Calculate Sine, Cosine, and Tangent

Using the unit circle and special triangles, you can find the values for the sine, cosine, and tangent of common angles:

0°, 90°, 180°, 270° (Angles on the Axes)

• At 0° (0 radians), the coordinates are (1, 0):
  • sin⁡(0°)=0
  • cos⁡(0°)=1
  • tan⁡(0°)=0
• At 90° (π/2 radians), the coordinates are (0, 1):
  • sin⁡(90°)=1
  • cos⁡(90°)=0
  • tan⁡(90°) is undefined (division by zero)
• At 180° (π radians), the coordinates are (-1, 0):
  • sin⁡(180°)=0
  • cos⁡(180°)=−1
  • tan⁡(180°)=0
• At 270° (3π/2 radians), the coordinates are (0, -1):
  • sin⁡(270°)=−1
  • cos⁡(270°)=0
  • tan⁡(270°) is undefined (division by zero)

30°, 45°, 60° (Angles in Special Triangles)

• For 30° (π/6 radians):
  • \(sin(30°) = \frac{1}{2}\)
  • \(cos(30°) = \frac{\sqrt{3}}{2}\)
  • \(tan(30°) = \frac{\sqrt{3}}{3}\)
• For 45° (π/4 radians):
  • \(sin(45°) = \frac{\sqrt{2}}{2}\)
  • \(cos(45°) = \frac{\sqrt{2}}{2}\)
  • \(tan(45°) = 1\)
• For 60° (π/3 radians):
  • \(sin(60°) = \frac{\sqrt{3}}{2}\)
  • \(cos(60°) = \frac{1}{2}\)
  • \(tan(60°) = \sqrt{3}\)

Step 4: Compile the Table

Here is a basic trigonometry table for common angles:

Angle (°)	Angle (radians)	Sine (sin)	Cosine (cos)	Tangent (tan)
0°	0	0	1	0
30°	π/6	1/2	√3/2	√3/3
45°	π/4	√2/2	√2/2	1
60°	π/3	√3/2	1/2	√3
90°	π/2	1	0	Undefined
180°	π	0	-1	0
270°	3π/2	-1	0	Undefined
360°	2π	0	1	0

Step 5: Verify Your Calculations

Double-check your values with a scientific calculator or trigonometry reference to ensure accuracy.

By following these steps, you can create a trigonometry table by hand.

Frequently Asked Questions

What are the types of trigonometric functions?

In trigonometry, there are 6 different trigonometric functions which are given below:

1. Sin function
2. Cos function
3. Tan function
4. Cot function
5. Cosec function
6. Sec function

How to you find the value of trigonometric functions?

All the trigonometric functions are based to the sides of the triangle and their values. The value of trigonometric functions can be easily found by using the following formulas:

• Sin = Opposite/Hypotenuse
• Cos = Adjacent/Hypotenuse
• Tan = Opposite/Adjacent
• Cot = 1/Tan = Adjacent/Opposite
• Cosec = 1/Sin = Hypotenuse/Opposite
• Sec = 1/Cos = Hypotenuse/Adjacent