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

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)
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