University:
York University
Course:
MATH 1013 | Applied Calculus
Academic year:

2023
Views:

225

Pages:

3
Author:

Niklas

IV. Trigonometric Graphs (Ch. 4) I. TRIGONOMETRIC PARENT FUNCTION GRAPHS AND PROPERTIES period - distance along the domain that is a measure of one cycle amplitude - the vertical distance the curve reaches from center axis phase shift - how far the curve is shifted horizontally or vertically from the usual position frequency - the number of complete cycles that happen every second sine function f(x) = sin x domain: (-∞, ∞) range: [-1, 1] odd period: 2π amplitude: 1 continuous: (-∞, ∞) cosine function f(x) = cos x domain: (-∞, ∞) range: [-1, 1] even period: 2π amplitude: 1 continuous: (-∞, ∞) tangent function domain: {x | x ≠ (2n + 1)π/2, n ∈ Z} range: (-∞, ∞) odd period: π amplitude: none asymptotes: x = (2n + 1)π/2, n ∈ Z I. TRIGONOMETRIC PARENT FUNCTION GRAPHS AND PROPERTIES period - distance along the domain that is a measure of one cycle amplitude - the vertical distance the curve reaches from center axis phase shift - how far the curve is shifted horizontally or vertically from the usual position frequency - the number of complete cycles that happen every second sine function f(x) = sin x domain: (-∞, ∞) range: [-1, 1] odd period: 2π amplitude: 1 continuous: (-∞, ∞) cosine function f(x) = cos x domain: (-∞, ∞) range: [-1, 1] even period: 2π amplitude: 1 continuous: (-∞, ∞) tangent function f(x) = tan x domain: {x | x ≠ (2n + 1)π/2, n ∈ Z} range: (-∞, ∞) odd period: π amplitude: none asymptotes: x = (2n + 1)π/2, n ∈ Z cotangent function f(x) = cot x domain: {x | x ≠ nπ, n ∈ Z} range: (-∞, ∞) odd period: π amplitude: none asymptotes: x = nπ, n ∈ Z secant function f(x) = sec x domain: {x | x ≠ (2n + 1)π/2, n ∈ Z} range: (-∞, -1] U [1, ∞) even period: 2π amplitude: none asymptotes: x = (2n + 1)π/2, n ∈ Z cosecant function f(x) = csc x domain: {x | x ≠ nπ, n ∈ Z} range: (-∞, -1] U [1, ∞) odd period: 2π amplitude: none asymptotes: x = nπ, n ∈ Z II. TRANSFORMATIONS y = a trig(bx - c) + d for sine and cosine, let P represent the period of the parent, the transformed period is: P' = P/b |a| is the amplitude if a < 0, there is a reflection over the x-axis d is the vertical shift c/b is the horizontal phase shift f(x) = 2sin(x) + 3 period: 2π amplitude: 2 transformations: vs up 3 g(x) = 2cos(3x) period: 2π/3 amplitude: 2 transformations: none h(x) = tan(x - π/4) period: π amplitude: none transformations: hps right π/4 f(x) = sec(x) - 4 period: 2π amplitude: none transformations: vs down 4