Unit 4 Lesson 5: Trigonometric Functions Vocabulary and Graphing Concepts

Flashcards covering key vocabulary and transformation concepts for sine and cosine functions based on lecture notes.

Amplitude

The distance from the midline to the highest point of a sine or cosine graph.

Period

The length of one cycle of a trigonometric function, which is $2 ext{\pi}$ for the standard sine and cosine functions.

Horizontal shift

Represented by the variable $c$ in trigonometric translations, indicating a shift along the x-axis.

Vertical shift

Represented by the variable $d$ in trigonometric translations, indicating a shift along the y-axis.

Amplitude of $y = 2 \sin(x)$

The amplitude is $2$.

Period of $y = \cos(\frac{x}{3})$

The length of one cycle, calculated as 6\text{\pi}.

Amplitude of y = \frac{1}{2} \sin(x - \frac{\text{\pi}}{3})

The amplitude is $\frac{1}{2}$.

Horizontal shift of y = \frac{1}{2} \sin(x - \frac{\text{\pi}}{3})

A translation to the right by \frac{\text{\pi}}{3}.

Amplitude of y = 2 \cos(x - \frac{\text{\pi}}{2})

The amplitude is $2$, with a shift to the right by \frac{\text{\pi}}{2}.

Vertical translation of $y = 2 \cos(x) - 5$

A vertical shift downward by $5$ units.

Midline shift of $y = 2 + 3 \cos(2x)$

The graph is shifted up by $2$ units, changing the midline from $y = 0$ to $y = 2$.