Key Features of Sine and Cosine

Front

What is the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak or trough. It is always a positive value.

Front

Write the general equation for a sine function.

Back

The general equation 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.

Front

What is the period of a sine or cosine function?

Back

The period is the distance along the x-axis for one complete cycle of the wave. It is calculated as \( \frac{2\pi}{|B|} \) in the general equation.

Front

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

Back

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

Front

Back

The amplitude is 3, as amplitude is always taken as a positive value regardless of the sign in front.

Front

Back

The period is \( \frac{2\pi}{4} = \frac{\pi}{2} \).

Front

What is the effect of changing the value of A in the equation y = A sin(Bx)?

Back

Changing A affects the amplitude of the wave. A larger A results in a taller wave, while a smaller A results in a shorter wave.

Front

What is the effect of changing the value of B in the equation y = A sin(Bx)?

Back

Changing B affects the period of the wave. A larger B results in a shorter period (more cycles in a given interval), while a smaller B results in a longer period.

Front

Back

The vertical shift is 2, moving the entire graph up by 2 units.

Front

Identify the sine function from the following: y = sin(x), y = cos(x).

Back

y = sin(x) is the sine function.