Trigonometric and Parent Function Transformations

This set of vocabulary flashcards covers trigonometric function parameters, transformations of functions, coordinate directions, and basic statistical identities based on the lecture notes.

$B$ (in $y = \pm A \sin(B(x + C)) \pm D$)

It determines the period of the graph.

Period of a sine or cosine graph

How long it takes for one cycle

Shape of a sine wave

A repeating curve that starts at the midline, rises to a maximum, falls through the midline to a minimum, and returns to the midline

Odd function symmetry

Symmetry through the origin

$$f(-x)$$

Reflect the graph over the $y$-axis.

$af(x)$ where $a > 1$

Vertical sketch

$$f(x) \rightarrow -\infty$$

Down

$C$ (in $y = \pm A \sin(B(x + C)) \pm D$)

The phase shift, moving the graph left or right

$af(x)$ where $0 < a < 1$

Vertical shrink

$D$ (in $y = \pm A \sin(B(x + C)) \pm D$)

The baseline or vertical shift, moving the graph up or down

Margin of error

Equivalent to $20$

$$f(x) - c$$

Shift the graph down $c$-units

Pythagorean Trig Identity

$$\sin^2(\theta) + \cos^2(\theta) = 1$$

Domain

The set of input or $x$-values for which a relation is defined.

$$x \rightarrow -\infty$$

Left

Range

The set of $y$-values for which a relation is defined.

$f(ax)$ where $0 < a < 1$

Horizontal sketch

$z$-score formula

$$\frac{\text{value} - \text{mean}}{\sigma}$$

Radians into degrees conversion

Multiply by $\frac{180}{\pi}$

$f(ax)$ where $a > 1$

horizontal shrink

$$f(x - c)$$

It moves right $c$ units

$A$ (in $y = \pm A \sin(B(x + C)) \pm D$)

The amplitude of the graph.