Trigonometry Table deals with various angles and their corresponding trigonometric ratios. The trigonometric values of various standard angles are useful to have in-hand as they are used heavily in many real-life applications in geometrical, navigational (e.g. in ships and lighthouses), and various other areas. Some standard angles have been universally used which include 0°, 30°, 45°, 60°, and 90°. These have heavy applications and are commonly used which make knowing their value even more important.
Hence, a Trigonometric Table has been carefully formulated to tabulate the trigonometric values of the various trigonometric ratios of standard angles. This table is introduced in trigonometry class 10 itself.
The Trigonometric Table is simply a collection of trigonometric values of various standard angles including 0°, 30°, 45°, 60°, 90°, sometimes with other angles like 180°, 270°, and 360° included, in a tabular format. Because of patterns existing within trigonometric ratios and even between angles, it is easy to both predict the values of the table and use the table as a reference to calculate trigonometric values for various other angles.
The trigonometric functions are namely sine function, cosine function, tan function, cot function, sec function, and cosec function.
The Trigonometric Ratios Table is as follows:
|
𝚹 (°) |
0° |
30° |
45° |
60° |
90° |
180° |
270° |
360° |
|
𝚹(rad) |
0 |
π/6 |
π/4 |
π/3 |
π/2 |
π |
3π/2 |
2π |
|
Sine |
0 |
1/2 |
1/√2 |
√3/2 |
1 |
0 |
-1 |
0 |
|
Cosine |
1 |
√3/2 |
1/√2 |
1/2 |
0 |
-1 |
0 |
1 |
|
Tan |
0 |
1/√3 |
1 |
√3 |
∞ |
0 |
∞ |
0 |
|
Cot |
∞ |
√3 |
1 |
1/√3 |
0 |
∞ |
0 |
∞ |
|
Cosec |
∞ |
2 |
√2 |
2/√3 |
1 |
∞ |
-1 |
∞ |
|
Sec |
0 |
2/√3 |
√2 |
2 |
∞ |
-1 |
∞ |
-1 |
A few things to be noted in the Trigonometry Table are,
The Trigonometry table might seem intimidating at first, but it can be easily generated by only the values of sine for the 8 standard angles.
Before generating the table, certain formulas must be followed and hence should be at the back of your head.
tan x = sin x/cos x
1/sin x = cosec x
1/cos x = sec x
1/tan x = cot x
Step 1
Write the angles 0°, 30°, 45°, 60°, 90° in ascending order and assign them values 0, 1, 2, 3, 4 according to the order.
so,
0° ⟶ 0 30° ⟶ 1 45° ⟶ 2 60° ⟶ 3 90° ⟶ 4
Then divide the values by 4 and square root the entire value.
0° ⟶ √0/2 30° ⟶ 1 /2 45° ⟶ 1/ √2 60° ⟶ √3/2 90° ⟶ √(4/4)
This gives the values of sine for these 5 angles.
Now for the remaining three use
sin (180° − x) = sin x
sin (180° + x) = -sin x
sin (360° − θ) = -sin x
Implying,
sin (180° − 0) = sin 0
sin (180° + 90) = -sin 90
sin (360° − 0) = -sin 0
| Sine | 0 | 1/2 | 1/√2 | √3/2 | 1 | 0 | -1 | 0 |
Step 2
sin (90° – x) = cos x
Use this formula to compute values for cos x.
For eg: cos 45° = sin (90° – 45°)
cos 45° = sin 45°
Similarly,
cos 30° = sin (90°-30°)
cos 30° = sin 60°
Using this, you can easily find out the value of cos x row.
| Cosine | 1 | √3/2 | 1/√2 | 1/2 | 10 | -1 | 0 | 1 |
Step 3
tan x = sin x/cos x
Hence, the tan row can be generated.
| Tan | 0 | 1/√3 | 1 | √3 | ∞ | 0 | ∞ | 0 |
Step 4
cot x = 1/tan x
Use the relation to generate the cotan row
| Cot | ∞ | √3 | 1 | 1/√3 | 0 | ∞ | 0 | ∞ |
Step 5
cosec x = 1/sin x
| Cosec | ∞ | 2 | √2 | 2/√3 | 1 | ∞ | -1 | ∞ |
Step 6
sec x = 1/cos x
| Sec | 0 | 2/√3 | √2 | 2 | ∞ | -1 | ∞ | -1 |