Similarly, the sine of the angle B is

Similarly, the tangent of the angle B is

Proof Consider a right triangle ABC with angle C equal to 90 degrees. From the Pythagorean theorem it follows that

From the definition of the sine of the angle A we have that sin A = BC/AB. Let's plug this result into the expression for BC:

From the theorem 14.1 we know that the cosine of A depends only on the degree measure of the angle A. Therefore so is the sine of A.

Similarly we have that

Therefore tan A depends only on the degree measure of the angle A as well.

Theorem 15.2 Let ABC be a right triangle with angle C equal to 90 degrees. Then for any acute angle A the following is true:

Proof From the Pythagorean theorem we have that

Let's divide both sides of this equation by

But we already know that sin A = BC/AB and cos A = AC/AB. Therefore

The other two equalities easily follow from the first one.