"Explain why the name pythagorean identity is appropriate"

Question of the Day: "Explain why the name pythagorean identity is appropriate"

Well for starters, the formula for the pythagorean theorem (used for a triangle) is a² +b² =c² ; where a and b are the sides of a triangle and c is the hypothenuse. It allows people to identify the sides of a Right triangle.





Not only do we use the pythagorean identity in Algebra, we use the pythagorean identity in Algebra II/Trig. How is this possible ?

   We create a circle like the figure shown on the left, we use one side of the diameter and create a triangle from the "x and y axis" (of the cicle). The Blue line can be identified as the radius of

the circle or as the hypothenuse of the right triangle. We can say, that the radius of the circle is 1. But how does the Pythagorean apply to Trig.? Its simple, let us express sin and cos to the triangle; 

 

 




 

 

sin(ɵ) is expressed as opposite / (over) hypotenuse which is ; y / 1 = y

and

cos(ɵ) is expressed as adjacent / hypotenuse which is equal to x / 1 = x

The Pythagorean Identity is an appropriate name because we can use the formula; a² +b² =c² to say that sin²(ɵ) + cos²(ɵ) = 1 *our trig. formula* The Pythagorean Theorem has simply developed to help us excell in Algebra II/Trig. We can now identify cot, sec, csc, and tan by using the Pythagorean Identity's help.

Example:

sec(ɵ) = 1 / cos(ɵ)

csc(ɵ) = 1 / sin(ɵ)

cot(ɵ) = 1 / tan(ɵ) which is equal to cos(ɵ) / sin(ɵ)