# 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 ° $\frac{1}{2}$ $\frac{\sqrt{3}}{2}$ $\frac{\sqrt{3}}{3}$ 45 ° $\frac{\sqrt{2}}{2}$ $\frac{\sqrt{2}}{2}$ 1 60 ° $\frac{\sqrt{3}}{2}$ $\frac{1}{2}$ $\sqrt{3}$ 90 ° 1 0 ∞ 120 ° $\frac{\sqrt{3}}{2}$ $-\frac{1}{2}$ $-\sqrt{3}$ 135 ° $\frac{\sqrt{2}}{2}$ $-\frac{\sqrt{2}}{2}$ -1 150 ° $\frac{1}{2}$ $-\frac{\sqrt{3}}{2}$ $-\frac{\sqrt{3}}{3}$ 180 ° 0 -1 0 210 ° $-\frac{1}{2}$ $-\frac{\sqrt{3}}{2}$ $\frac{\sqrt{3}}{3}$ 225 ° $-\frac{\sqrt{2}}{2}$ $-\frac{\sqrt{2}}{2}$ 1 240 ° $-\frac{\sqrt{3}}{2}$ $-\frac{1}{2}$ $\sqrt{3}$ 270 ° -1 0 -∞ 300 ° $-\frac{\sqrt{3}}{2}$ $\frac{1}{2}$ $-\sqrt{3}$ 315 ° $-\frac{\sqrt{2}}{2}$ $\frac{\sqrt{2}}{2}$ -1 330 ° $-\frac{1}{2}$ $\frac{\sqrt{3}}{2}$ $-\frac{\sqrt{3}}{3}$ 360 ° 0 1 0