U6: A,B & C (Algebra 2H)

periodic function

A function that repeats its values at regular intervals or periods, such as sine and cosine functions.

sine = 0

tangent has a value of 0 whenever

cos = 0

tangent is not defined and has a vertical asymptote whenever

even function

function type of cosine

odd function

function type of sine

odd function

function type of tangent

point: (1, 0)

0 radians

point: (0, 1)

π/2 radians

point: (-1, 0)

π radians

point: (0, -1)

3π/2 radians

point: (1/2, √3/2)

π/3 radians

point: (√2/2, √2/2)

π/4 radians

point: (√3/2, 1/2)

π/6 radians

period

The length of one complete cycle of a periodic function, typically measured in radians. For sine and cosine functions, the period is 2π.

30-60-90 triangle

A right triangle where the 1. hypotenuse segment=2× 2. 30-90 segment=√3:2× 3. 90-60 segment=x.

isosceles right triangle

A right triangle where the 1. hypotenuse segment=√2x 2. both legs=x

radian

A unit of angular measure used in mathematics, defined as the angle subtended at the center of a circle by an arc equal in length to the radius of the circle. One complete revolution corresponds to 2π radians.

Unit Circle

A circle with a radius of one, centered at the origin of the coordinate plane, used to define trigonometric functions.

cos θ

X/R where X is the length of the adjacent side and R is the length of the hypotenuse in a right triangle.

sin θ

Y/R where Y is the length of the opposite side and R is the length of the hypotenuse in a right triangle.

tan θ

Y/X where Y is the length of the opposite side and X is the length of the adjacent side in a right triangle.

Pythagorean Theorem

In a right triangle, R² = X² + Y².

Pythagorean Identity

The relationship that states sin² θ + cos² θ = 1 for any angle θ, derived from the Pythagorean Theorem.