# Trigonometric table

As its name implies, it is a table where the values of sines, cosines and tangents of the notable angles (from 0 ° to 360 °). With it we can perform calculations in trigonometry without using a calculator.

## Trigonometric ratios of 0°, 30°, 60 ° and 90 °.

Let's consider the following triangle: Let's calculate the following values: sin (30 °), sin (60 °), cos (30 °), cos (60 °), tg (30 °), tg (60 °).

Remembering that:

• sin α = opposite leg / hypotenuse
• cos α = adjacent leg / hypotenuse
• tg α = opposite leg / adjacent leg = without α / cos α

We have:

• sin (30 °) = a / 2a = 1/2
• cos (30 °) = (a√3) / 2a = √3 / 2
• tg (30 °) = (1/2) / (√3 / 2) = 1 / √3
• sin (60 °) = (a√3) / 2a = √3 / 2
• cos (60 °) = a / 2a = ½
• tg (60 °) = (√3 / 2) / (1/2) = √3

## Trigonometric ratios of 45°

Now let's consider the following right triangle: Let's calculate the values of sin (45 °), cos (45 °) and tg (45 °):

• sin (45 °) = a / (a√2) = 1 / √2
• cos (45 °) = a / (a√2) = 1 / √2
• tg (45 °) = (1 / √2) / (1 / √2) = 1

## Values of the trigonometric functions of the notable angles

 Angle Sine Cosine Tangent 0 ° 0 1 0 30 °   45 °  1 60 °   90 ° 1 0 ∞ 120 °   135 °  -1 150 °   180 ° 0 -1 0 210 °   225 °  1 240 °   270 ° -1 0 -∞ 300 °   315 °  -1 330 °   360 ° 0 1 0