Fundamental identities are mathematical equations that express the relationship between trigonometric functions. They are considered fundamental because they form the basis of many other trigonometric equations and are essential for solving trigonometric problems.
The most commonly used fundamental identities include the Pythagorean identities, sum and difference identities, double angle identities, and half angle identities.
Fundamental identities are derived from the unit circle, which is a circle with a radius of 1 centered at the origin of a coordinate plane. By using the relationships between the coordinates of points on the unit circle, the fundamental identities can be derived.
Fundamental identities are important because they allow us to simplify complex trigonometric expressions, solve trigonometric equations, and prove other trigonometric identities. They are also used in various applications such as physics, engineering, and navigation.
Memorizing all the fundamental identities can be challenging, but with practice and repetition, it can be achieved. It is helpful to group them by type and understand the patterns and relationships between them. Also, using mnemonic devices or creating flashcards can aid in memorization.