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:

exercise 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:

exercise triangle2

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

AngleSineCosineTangent
0 °010
30 °
45 °1
60 °
90 °10
120 °
135 °-1
150 °
180 °0-10
210 °
225 °1
240 °
270 °-10-∞
300 °
315 °-1
330 °
360 °010