Lecture 7 Periodic Functions and Trigonometry

These flashcards cover key concepts related to periodic functions and trigonometric identities as discussed in the lecture.

Periodic Function

A function f(x) is periodic if it satisfies f(x) = f(x + period) for some fixed period.

Cosine Function

A periodic function defined as the x-coordinate of a point on the unit circle.

Sine Function

A periodic function defined as the y-coordinate of a point on the unit circle.

Unit Circle

A circle with a radius of 1, used to define sine and cosine functions.

Hypotenuse

The longest side of a right triangle, opposite the right angle.

Adjacent Side

The side next to the angle of interest in a right triangle.

Opposite Side

The side opposite the angle of interest in a right triangle.

Pythagorean Identity

The relationship sin²(θ) + cos²(θ) = 1 for any angle θ.

Angle in Radians

An angle measure based on the radius of a circle, where 2π radians equals 360 degrees.

Finding Cosine from Sine

If sin(x) is known, cosine can be determined using the identity cos²(x) = 1 - sin²(x).