How to calculate a cosine

How to calculate a cosine

Cosine call trigonometrical function of a corner. It is defined geometrically by means of a single circle or as result of a ratio of the parties of a rectangular triangle. It is possible to calculate a cosine also through other trigonometrical functions, by means of the calculator or Bradis's tables.

It is required to you

  • - calculator;
  • - Bradis's tables;
  • - concept of Pythagorean theorem;
  • - trigonometrical identities;
  • - ruler.


1. Measure or count a corner which cosine needs to be calculated. Switch the engineering calculator to calculations in degrees, gain this value on its screen and pressing of the button calculate a cosine. If there is no such calculator, find value of a corner in appropriate section of tables of Bradis and find his cosine.

2. Calculate a cosine of the angle which represents turn of radius of a circle with the center at the beginning of coordinates concerning abscissa axis. For this purpose find an abscissa of a point of intersection of the radius limiting a corner with a circle which will be equal to a cosine of this corner. If a circle not single, divide the received abscissa into value of radius.

3. Find value of a cosine of an acute angle in a rectangular triangle. Define what of its parties are legs (the corner between them is equal 90 ˚). The third party will be a hypotenuse. To find a cosine of an acute angle, measure length of a leg, adjacent to it, and hypotenuse length, using for this purpose a ruler, or find the unknown party on two known, using Pythagorean theorem. The cosine of an acute angle will be equal to the relation of an adjacent leg to a hypotenuse. For example, if length of an adjacent leg is equal to 5 cm, and length of a hypotenuse is 10 cm, then the cosine of this corner is equal to 5/10=0.5. It is a cosine of the angle 60º.

4. Determine a cosine of the angle by its values for others trigonometrical functions. If the sine of the angle α that its cosine is known count, having taken away 1 square of a sine from number, and take the square root cos(α)= from the received result √ (1-sin² (α)). For example, if the sine of the angle is equal 0.6, then using the known formula, receive cos(α)= √ (1-0.6²)= √ (1-0.36) = √0.64=0.8.

5. Calculate a cosine at the known tangent of angle. For this purpose divide number 1 into the sum of 1 and a tangent square, and take a square root from the received result: cos(α)= √ (1 / (1+tg² (α))). For example, if the tangent of angle is equal 1, then its cosine to cos(α)= √ (1 / (1+1²)) =1 / √ 2.

Author: «MirrorInfo» Dream Team