This chapter provides the trigonometric table presenting the values of trigonometric functions.
Trigonometry is one of the most important concepts in mathematics, electrical engineering, electronics, civil engineering, mechanical engineering, and physics. It helps us determine unknown sides and angles of triangles and is widely used in circuit analysis, AC waveforms, surveying, navigation, robotics, satellite communication, computer graphics, and solar power plant design.
What is Trigonometry?
Trigonometry is the branch of mathematics that studies the relationship between the angles and sides of a triangle.
The word Trigonometry comes from the Greek words –
- Tri = Three
- Gon = Angle
- Metron = Measure
Therefore, Trigonometry means the measurement of triangles.
Standard Angles
The trigonometry table is generally prepared for these standard angles –
| Degree | Radian |
| 0° | 0 |
| 30° | π/6 |
| 45° | π/4 |
| 60° | π/3 |
| 90° | π/2 |
Trigonometry Table (0° to 90°)
The trigonometry table for 0 to 90 degrees angles for all six trigonometric functions is shown below –
| Angle | 0° | 30° | 45° | 60° | 90° |
| sin θ | 0 | 1/2 | √2/2 | √3/2 | 1 |
| cos θ | 1 | √3/2 | √2/2 | 1/2 | 0 |
| tan θ | 0 | 1/√3 | 1 | √3 | Undefined |
| cot θ | Undefined | √3 | 1 | 1/√3 | 0 |
| sec θ | 1 | 2/√3 | √2 | 2 | Undefined |
| cosec θ | Undefined | 2 | √2 | 2/√3 | 1 |
ASTC Rule (Sign of Trigonometric Functions)
A simple way to remember the signs of trigonometric functions in each quadrant is the ASTC rule represented in the following figure –
Trigonometry Table (0° to 360°)
The trigonometry table for 0 to 360 degrees angles for all six trigonometric functions is shown below –
| Angle (°) | Radian | sin θ | cos θ | tan θ | cosec θ | sec θ | cot θ |
| 0° | 0 | 0 | 1 | 0 | Undefined | 1 | Undefined |
| 30° | π/6 | 1/2 | √3/2 | 1/√3 | 2 | 2/√3 | √3 |
| 45° | π/4 | √2/2 | √2/2 | 1 | √2 | √2 | 1 |
| 60° | π/3 | √3/2 | 1/2 | √3 | 2/√3 | 2 | 1/√3 |
| 90° | π/2 | 1 | 0 | Undefined | 1 | Undefined | 0 |
| 120° | 2π/3 | √3/2 | -1/2 | -√3 | 2/√3 | -2 | -1/√3 |
| 135° | 3π/4 | √2/2 | -√2/2 | -1 | √2 | -√2 | -1 |
| 150° | 5π/6 | 1/2 | -√3/2 | -1/√3 | 2 | -2/√3 | -√3 |
| 180° | π | 0 | -1 | 0 | Undefined | -1 | Undefined |
| 210° | 7π/6 | -1/2 | -√3/2 | 1/√3 | -2 | -2/√3 | √3 |
| 225° | 5π/4 | -√2/2 | -√2/2 | 1 | -√2 | -√2 | 1 |
| 240° | 4π/3 | -√3/2 | -1/2 | √3 | -2/√3 | -2 | 1/√3 |
| 270° | 3π/2 | -1 | 0 | Undefined | -1 | Undefined | 0 |
| 300° | 5π/3 | -√3/2 | 1/2 | -√3 | -2/√3 | 2 | -1/√3 |
| 315° | 7π/4 | -√2/2 | √2/2 | -1 | -√2 | √2 | -1 |
| 330° | 11π/6 | -1/2 | √3/2 | -1/√3 | -2 | 2/√3 | -√3 |
| 360° | 2π | 0 | 1 | 0 | Undefined | 1 | Undefined |
Decimal Value Trigonometry Table
The trigonometry table for 0 to 360 degrees angles for three fundamental trigonometric functions with their decimal values is shown below –
| Angle | sin θ | cos θ | tan θ |
| 0° | 0.0000 | 1.0000 | 0.0000 |
| 30° | 0.5000 | 0.8660 | 0.5774 |
| 45° | 0.7071 | 0.7071 | 1.0000 |
| 60° | 0.8660 | 0.5000 | 1.7321 |
| 90° | 1.0000 | 0.0000 | Undefined |
| 120° | 0.8660 | -0.5000 | -1.7321 |
| 135° | 0.7071 | -0.7071 | -1.0000 |
| 150° | 0.5000 | -0.8660 | -0.5774 |
| 180° | 0.0000 | -1.0000 | 0.0000 |
| 210° | -0.5000 | -0.8660 | 0.5774 |
| 225° | -0.7071 | -0.7071 | 1.0000 |
| 240° | -0.8660 | -0.5000 | 1.7321 |
| 270° | -1.0000 | 0.0000 | Undefined |
| 300° | -0.8660 | 0.5000 | -1.7321 |
| 315° | -0.7071 | 0.7071 | -1.0000 |
| 330° | -0.5000 | 0.8660 | -0.5774 |
| 360° | 0.0000 | 1.0000 | 0.0000 |