Math 1103 Transformations of Trigonometric Graphs

These flashcards cover key concepts related to transformations of trigonometric graphs, including domains, ranges, periods, and inverse functions.

Amplitude (|A|)

The maximum distance from the midline of a trigonometric graph.

Period (|ω|)

The length of one complete cycle of the trigonometric function.

Phase Shift (φ/ω)

The horizontal shift left or right for a trigonometric graph.

Domain of sin(x)

(−∞, ∞)

Range of sin(x)

[−1, 1]

Period of sin(x)

2π

Domain of arcsin(x)

[−1, 1]

Range of arcsin(x)

[−π/2, π/2]

Domain of cos(x)

(−∞, ∞)

Range of cos(x)

[−1, 1]

Domain of arccos(x)

[−1, 1]

Range of arccos(x)

[0, π]

Domain of tan(x)

x ≠ ± kπ/2, k is an odd integer.

Range of tan(x)

(−∞, ∞)

Period of tan(x)

π

Domain of arctan(x)

(−∞, ∞)

Range of arctan(x)

(−π/2, π/2)

Domain of cot(x)

x ≠ ±kπ, k is an integer.

Range of cot(x)

(−∞, ∞)

Period of cot(x)

π

Domain of arccot(x)

(−∞, ∞)

Range of arccot(x)

(0, π)

Domain of sec(x)

x ≠ ± kπ/2, k is an odd integer.

Range of sec(x)

(−∞, 1] ∪ [1, ∞)

Period of sec(x)

2π

Domain of arcsec(x)

(−∞, −1] ∪ [1, ∞)

Range of arcsec(x)

[0, π/2) ∪ (π/2, π]

Domain of csc(x)

x ≠ ±kπ, k is an integer.

Range of csc(x)

(−∞, 1] ∪ [1, ∞)

Period of csc(x)

2π

Domain of arccsc(x)

(−∞, −1] ∪ [1, ∞)

Range of arccsc(x)

[−π/2, 0) ∪ (0, π/2]