Sine and tangent angle

The ratio of the opposite leg to the hypotenuse is called the sine of the acute angle of a right triangle.



The sine of the angle α is denoted by: sin α.



The tangent of the angle of a right-angled triangle is the ratio of the opposite leg to the adjacent leg. The tangent of the angle α is indicated: tg α.



Theorem.

The sinus and tanngs of the angle, like the cosine, depend only on the angle.

Evidence.

Let ABC be a given right triangle, then by the Pythagorean theorem



a



Then



And since cos depends only on the magnitude, sin also depends only on the magnitude.



Divide the numerator and denominator by AB:



And since cos and sin depend only on the angle, tg also depends only on the angle. The theorem is proved.