Question

Where does Pythagorean identities and also how it relates to the right triangles

Answer 1

Answer:

The Pythagorean identities are

$sin^{2} x + cos^{2} x = 1\\1+ tan^{2} x = sec^{2} x\\1 + cot^{2} x = csc^{2} x\\where\\csc x = \frac{1}{sinx} \\cot x = \frac{cosx}{sinx} or \frac{1}{tanx} \\tan x = \frac{1}{cotx} or \frac{sinx}{cosx} \\sec x = \frac{1}{cotx}$

No matter what the value of x (the angle degree amount) is, sin²x+cos²x is equal to 1

When given a side length of a right triangle you will be able to use one of these identities to find the angle amount

Answer 2

Answer:

A pythagorean identity means that for any angle $\theta$, $sin^2\theta+cos^2\theta=1$.

This also means $1+tan^2\theta=sec^2\theta \mbox{ and } 1+cot^2\theta=csc^2\theta.$ The symbol, theta ($\theta$) represents one of the acute angles in the right triangle. The hypotenuse (familiarly c in the regular pythagorean theorem) is 1. The triangle base is $cos\theta$, and the height (side perpendicular to the base, making a right angle) is $sin\theta$. The angle theta is opposite the $sin\theta$ side.

Step-by-step explanation:

The pythagorean theorem applies to right triangles, which always have a 90 degree angle. Pythagorean identities are used to simplify trigonometric expressions/evaluate trig functions and to find the trig ratios in a right triangle.