pythagorean identities
sin²θ + cos²θ = 1tan²θ + 1 = sec²θ1 + cot²θ = csc²θ
Pythagorean identities are a set of trigonometric formulas in mathematics that relate to the Pythagorean theorem. These identities are specifically used to solve problems in trigonometry, particularly in finding the values of trigonometric functions of angles.
There are primarily two Pythagorean identities:
1. sin² θ + cos² θ = 1.
This identity demonstrates the relationship between sine and cosine functions. It states that the square of sine function and cosine function’s square added together equals 1. This identity is applicable to all values of θ.
2. tan² θ + 1 = sec² θ.
This Pythagorean identity relates tangent, secant, and 1. It states that the square of tangent function added to 1 equals the square of secant function. This identity is applicable to all values of θ except where cosine function is equal to zero.
These identities are fundamental and used widely in calculus, engineering, physics, and other related fields. They aid in simplifying complex equations and help solve problems where trigonometric functions are involved.
More Answers:
Unlocking the Secrets of the Unit Circle: How to Find Missing Coordinates Using TrigonometryMaster cofunction identities: Simplify Trigonometric Expressions using Complementary Angles
Mastering Trigonometric Even-Odd Identities: Simplifying Complex Expressions.