All Flashcards
Explain the relationship between sine and cosine.
Cosine is a sine function shifted left by .
Explain the concept of period.
The length of one complete cycle before repetition.
Explain the concept of frequency.
How many cycles occur in one unit of time.
Explain how the midline affects the graph.
It shifts the graph vertically up or down.
Explain how amplitude affects the graph.
It stretches or compresses the graph vertically.
Describe the symmetry of sine.
Odd symmetry; symmetric about the origin.
Describe the symmetry of cosine.
Even symmetry; symmetric about the y-axis.
Explain the effect of transformations on the period.
Horizontal stretches/compressions change the period.
Explain the effect of transformations on the amplitude.
Vertical stretches/compressions change the amplitude.
Relationship between period and frequency.
They are reciprocals of each other.
How to identify the period from a graph?
Measure the distance for one complete cycle.
How to identify the midline from a graph?
Average of the maximum and minimum y-values.
How to identify the amplitude from a graph?
Half the difference between max and min y-values.
What does a shift in the midline indicate?
A vertical translation of the function.
How does changing the period affect the graph?
It stretches or compresses the graph horizontally.
How does changing the amplitude affect the graph?
It stretches or compresses the graph vertically.
How to identify concave up sections?
Curve looks like a smile.
How to identify concave down sections?
Curve looks like a frown.
What does the graph of tell us about its derivative?
The derivative, , represents the slope of at each point.
What does the graph of tell us about its derivative?
The derivative, , represents the slope of at each point.
Sine vs. Cosine: Symmetry.
Sine: Odd | Cosine: Even
Sine vs. Cosine: Shift.
Cosine is sine shifted left by .
Amplitude vs. Midline.
Amplitude: Vertical distance from midline | Midline: Horizontal center.
Period vs. Frequency.
Period: Length of one cycle | Frequency: Cycles per unit time.
Concave Up vs. Concave Down.
Concave Up: Curve smiles | Concave Down: Curve frowns.
What are the differences between period and frequency?
Period: Time for one cycle | Frequency: Cycles per unit time
What are the differences between amplitude and midline?
Amplitude: Vertical distance from midline | Midline: Horizontal center of the wave
What are the differences between sine and cosine functions?
Sine: Starts at midline | Cosine: Starts at maximum/minimum
What are the differences between a vertical stretch and a horizontal stretch?
Vertical: Affects amplitude | Horizontal: Affects period
What are the differences between positive and negative amplitudes?
Positive: Starts increasing | Negative: Starts decreasing