Trigonometry Review + Derivatives of Trigonometric Functions

These flashcards cover key vocabulary and definitions from trigonometry and derivatives of trigonometric functions discussed in the lecture.

Unit Circle

A circle with a radius of 1 centered at the origin, described by the equation x² + y² = 1.

Radian

The standard unit of angular measure, defined as the angle subtended at the center of a circle by an arc equal in length to the radius.

Sinusoidal Functions

Functions whose graphs take the shape of a sine or cosine curve, expressed in the form f(x) = A sin(Bx) + D.

Amplitude

Half the distance between the maximum and minimum values of a sinusoidal function.

Period

The least time needed for a sinusoidal function to complete one cycle.

Phase Shift

A horizontal shift of a sinusoidal function, expressed in the form f(x) = A sin(B(x + C)) + D.

Derivative of sin x

The derivative of sin x with respect to x is cos x.

Derivative of cos x

The derivative of cos x with respect to x is -sin x.

Derivative of tan x

The derivative of tan x with respect to x is sec² x.

Secant Function

Defined as the reciprocal of the cosine function; sec(x) = 1/cos(x).

Cosecant Function

Defined as the reciprocal of the sine function; csc(x) = 1/sin(x).

Cotangent Function

Defined as the quotient of cosine and sine; cot(x) = cos(x)/sin(x).

Pythagorean Identity

An identity involving sine and cosine: sin²(x) + cos²(x) = 1.

Right Triangle

A triangle in which one angle measures 90 degrees. Trigonometric functions are often defined in terms of the sides of a right triangle.

Trigonometric Functions

Functions defined based on a right triangle (sine, cosine, tangent, etc.) that relate angle measures to side lengths.

Cycle

A complete sequence of sinusoidal values from maximum to minimum and back.