Math127 Graphs Of Other Trigonometric

Cosecant

The inverse of sine.

Secant

The inverse of cosine.

Amplitude

The absolute value of the coefficient in front of the sine or cosine function, indicating the height of the wave peaks.

Period

The length of one complete cycle of a trigonometric function, calculated as 2π divided by the coefficient of x.

Vertical Asymptote

A line where a function approaches infinity, typically occurring where the sine or cosine function crosses the x-axis.

Tangent

A trigonometric function that represents the ratio of the sine and cosine of an angle.

Cotangent

The inverse of tangent, representing the ratio of cosine to sine.

Graph of Sine Function

A wave-like graph oscillating between its amplitude values, starting from the origin.

Graph of Cosine Function

A wave-like graph that starts at its maximum amplitude value and oscillates between negative and positive amplitudes.

X-Intercept

The point where a graph crosses the x-axis, indicating that the function value is zero.

Cosecant Graph

The graph derived from the sine graph, with vertical asymptotes at each x-intercept of the sine function.

Secant Graph

The graph derived from the cosine graph, with vertical asymptotes at each x-intercept of the cosine function.

Tangent Graph

A periodic graph that includes vertical asymptotes, where it repeats every π units.

Cotangent Graph

A periodic graph that is the inverse of the tangent graph, also repeating every π units.

Transformations

Changes made to the basic trigonometric graphs, including shifts and stretches, based on their equations.

Phase Shift

The horizontal shift of a trigonometric graph, determined by the value being added or subtracted from x in the function.