How to calculate cosine
You will need
- - calculator;
- - tables of Bradis;
- - the concept of the Pythagorean theorem;
- - trigonometric identities;
- - line.
Measure or calculate the angle whose cosine you want to calculate. Switch the engineering calculator to calculations in degrees, type this value on its screen and press the button to calculate the cosine. If there is no such calculator, find the angle value in the corresponding section of the Bradis tables and find its cosine.
Calculate the cosine of the angle, which is the rotation of the radius of a circle with the center at the origin of coordinates relative to the x-axis. To do this, find the abscissa of the intersection point of the radius limiting the angle with the circle, which will be equal to the cosine of this angle. If the circle is not a single one, divide the obtained abscissa by the radius value.
Find the cosine value of the acute angle in a right triangle. Determine which of its sides are the legs (the angle between them is 90˚). The third party will be hypotenuse.To find the cosine of an acute angle, measure the length of the leg adjacent to it and the length of the hypotenuse using a ruler, or find the unknown side from the two known ones using the Pythagorean theorem. The cosine of an acute angle will be equal to the ratio of the adjacent leg to the hypotenuse. For example, if the length of the adjacent leg is 5 cm, and the length of the hypotenuse is 10 cm, then the cosine of this angle is 5/10 = 0.5. This is the cosine of 60º.
Determine the cosine of the angle from its values for other trigonometric functions. If the sine of the angle α is known, then calculate its cosine, subtracting the square of the sine from the number 1, and from the result, take the square root cos (α) = √ (1-sin² (α)). For example, if the sine of the angle is 0.6, then using the well-known formula, obtain cos (α) = √ (1-0.6²) = √ (1-0.36) = √0.64 = 0.8.
Calculate the cosine at a known tangent of the angle. To do this, divide the number 1 by the sum of 1 and the square of the tangent, and from the result, take the square root: cos (α) = √ (1 / (1 + tg² (α))). For example, if the tangent of an angle is 1, then its cosine is cos (α) = √ (1 / (1 + 1²)) = 1 / √2.
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