General Form of a Sine or
Cosine Function:
Where:
Sine function:
• a affects amplitude.
• b affects period (or frequency).
• Cosine function:
• c affects phase shift.
• d affects vertical shift.
How the Parameters Affect the Graph:
• Amplitude (controlled by a): This stretches or compresses the graph vertically. The higher
the value of |a|, the larger the amplitude.
• Period (controlled by b): The period is the distance between the repeating cycles of the
graph. It is given by .
• Phase shift (controlled by c): This moves the graph left or right. The phase shift is .
• Vertical shift (controlled by d): This moves the graph up or down.
Similarities and Differences
Between Sine and Cosine:
• Both sine and cosine functions have
the same amplitude, period, and
general shape (smooth, wave-like).
• The main difference is in their
starting points: sine starts at 0,
while cosine starts at its maximum
value.
Cosine Function:
Where:
Sine function:
• a affects amplitude.
• b affects period (or frequency).
• Cosine function:
• c affects phase shift.
• d affects vertical shift.
How the Parameters Affect the Graph:
• Amplitude (controlled by a): This stretches or compresses the graph vertically. The higher
the value of |a|, the larger the amplitude.
• Period (controlled by b): The period is the distance between the repeating cycles of the
graph. It is given by .
• Phase shift (controlled by c): This moves the graph left or right. The phase shift is .
• Vertical shift (controlled by d): This moves the graph up or down.
Similarities and Differences
Between Sine and Cosine:
• Both sine and cosine functions have
the same amplitude, period, and
general shape (smooth, wave-like).
• The main difference is in their
starting points: sine starts at 0,
while cosine starts at its maximum
value.
