Express sine of an acute angle of a right triangle through the length of the sides of this figure.By definition, the sine of the angle (α) must be equal to the ratio of the side length (a), lying opposite it - the leg - to the side length (c), the opposed right angle - hypotenuse: sin (α) = a / c.
Find a similar formula for the cosine and the same angle.By definition, this value should be expressed by the ratio of the length of the part (b), adjacent to this angle (second leg), the length of the part (c), lying oppos
ite the right angle: cos (a) = a / c.
Rewrite equality arising from the Pythagorean theorem, so that there have been involved the relationship between the leg and a hypotenuse, derived in the previous two steps.To do this, first divide both sides of the original equation of this theorem (a² + b² = c²) by the square of the hypotenuse (a² / c² + b² / c² = 1), then the resulting equation can be rewritten in this way: (a / c) ² + (b/ c) ² = 1.
Replace in the resulting expression ratio of the lengths of the legs and the hypotenuse trigonometric functions, based on the formulas of the first and second step: sin² (a) + cos² (a) = 1. Express cosine of the resulting equation: cos (a) = √ (1 - sin² (a)).This problem can be considered solved in a general form.
If apart from the general solutions to get a numerical result, use, such as a calculator built into the operating system Windows.Link to get it to run in the "Standard" under "All Programs" menu of the main OS.This link is formulated succinctly - "Calculators."To be able to calculate with this program trigonometric functions include its "engineering" interface - press the key combination Alt + 2.
enter this under the sine of the angle and click on the interface labeled x² - soyou will build the initial value of the square.Then start typing * 1, press Enter, enter 1, and press Enter again - this way you subtract the square of the sine of the unit.Click on the button marked with the radical to take the square root and get the final result.