Trigonometric Functions Lecture Notes

A set of flashcards based on the lecture notes for trigonometric functions, covering key concepts, definitions, and identities.

Trigonometric Functions

Functions of an angle that relate the angles of a triangle to the ratios of its sides.

Terminal side

The location of an angle in standard position, where the angle opens from the initial side.

Initial side

The starting position of an angle before it opens to the terminal side.

sin θ

Ratio of the length of the opposite side to the hypotenuse in a right triangle.

cos θ

Ratio of the length of the adjacent side to the hypotenuse in a right triangle.

tan θ

Ratio of sin θ to cos θ, or the opposite side divided by the adjacent side.

csc θ

Reciprocal of sin θ, which is the ratio of the hypotenuse to the opposite side.

sec θ

Reciprocal of cos θ, which is the ratio of the hypotenuse to the adjacent side.

cot θ

Reciprocal of tan θ, or the adjacent side divided by the opposite side.

Fundamental Identities

Basic identities used to relate the trigonometric functions to one another.

Quadrant I

Where both sin θ and cos θ are positive.

Quadrant II

Where sin θ is positive and cos θ is negative.

Quadrant III

Where both sin θ and cos θ are negative.

Quadrant IV

Where sin θ is negative and cos θ is positive.

r = √(x² + y²)

The distance from the origin to the point (x,y) on the terminal side.

Similar triangles

Triangles that have the same shape, but may differ in size.

cot² θ + 1 = csc² θ

An identity illustrating the relationship between cotangent and cosecant.

tan² θ + 1 = sec² θ

An identity illustrating the relationship between tangent and secant.