Trig graphing

Here are some quick flashcard-style notes on Phase Shift, Period, Amplitude, and Vertical Shift in trigonometric functions:

Flashcard 1: Amplitude

• Definition: The height from the midline to the peak (or trough) of a wave.

• Formula: Given y = a \sin(bx + c) + d or y = a \cos(bx + c) + d,

• Amplitude = |a|

• Effect: Larger |a| → Taller wave, Smaller |a| → Shorter wave.

Flashcard 2: Period

• Definition: The length of one full cycle of the wave.

• Formula: \text{Period} = \frac{2\pi}{|b|} for sine and cosine.

• Effect:

• Larger |b| → Shorter period (more cycles).

• Smaller |b| → Longer period (fewer cycles).

Flashcard 3: Phase Shift

• Definition: A horizontal shift of the graph left or right.

• Formula: \text{Phase Shift} = -\frac{c}{b} (solve bx + c = 0).

• Effect:

• +c → Shift left.

• -c → Shift right.

Flashcard 4: Vertical Shift

• Definition: Moves the entire graph up or down.

• Formula: The value of d in y = a \sin(bx + c) + d.

• Effect:

• +d → Shift up.

• -d → Shift down.

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