Sine and Cosine Function Graphs

Front

What is the general form of a sine function?

Back

The general form of a sine function is: y = A sin(B(x - C)) + D, where A is the amplitude, B affects the period, C is the horizontal shift, and D is the vertical shift.

Tags

CCSS.HSF-IF.C.7E

Front

What is the general form of a cosine function?

Back

The general form of a cosine function is: y = A cos(B(x - C)) + D, where A is the amplitude, B affects the period, C is the horizontal shift, and D is the vertical shift.

Tags

CCSS.HSF-IF.C.7E

Front

How do you determine the amplitude of a sine or cosine function?

Back

The amplitude is the absolute value of A in the equations y = A sin(B(x - C)) + D or y = A cos(B(x - C)) + D.

Tags

CCSS.HSF-IF.C.7E

Front

What is the period of a sine or cosine function?

Back

The period is calculated as: Period = \frac{2\pi}{|B|}, where B is the coefficient of x in the function.

Tags

CCSS.HSF.TF.A.4

Front

What is the maximum value of a sine function?

Back

The maximum value of a sine function is A, where the function is in the form y = A sin(B(x - C)) + D.

Tags

CCSS.HSF-IF.C.7E

Front

What is the minimum value of a cosine function?

Back

The minimum value of a cosine function is D - A, where the function is in the form y = A cos(B(x - C)) + D.

Tags

CCSS.HSF-IF.C.7E

Front

If a sine function has a maximum at (5.1, 800) and a minimum at (2.9, 200), how do you find the amplitude?

Back

Amplitude = \frac{\text{Maximum} - \text{Minimum}}{2} = \frac{800 - 200}{2} = 300.

Front

What is the vertical shift in the function y = 3 sin(x) + 2?

Back

The vertical shift is 2, which moves the graph up by 2 units.

Tags

CCSS.HSF-IF.C.7E

Front

How do you find the horizontal shift of a sine function?

Back

The horizontal shift is determined by C in the equation y = A sin(B(x - C)) + D. If C is positive, the graph shifts to the right; if negative, it shifts to the left.

Tags

CCSS.HSF-IF.C.7E

Front

What is the effect of changing the value of B in the sine function?

Back

Changing B affects the period of the function. A larger B results in a shorter period, while a smaller B results in a longer period.

Tags

CCSS.HSF-IF.C.7E