Why use cosine power factor?

It's all to do with trigonometry. Apparent power is the vector-sum of true power and reactive power, and you can think of these three quantities forming a right-angled triangle (an oversimplification, but good enough for our purposes). Power factor is defined as the ratio of true power to apparent power, which corresponds to the ratio of adjacent to hypotenuse of this right-angled triangle. This ratio is called a cosine.