Sine and Cosine Graphs

Front

What is the period of the sine and cosine graphs?

Back

The period of the sine and cosine graphs is 2π.

Front

What effect does a negative amplitude (A value) have on the graph?

Back

A negative amplitude causes a reflection across the X-axis.

Front

What is the general form of the equation for a cosine graph?

Back

The general form is y = A cos(Bx + C) + D, where A is the amplitude, B affects the period, C is the phase shift, and D is the vertical shift.

Front

What is the equation of the graph if it is reflected across the X-axis?

Back

If the graph is reflected across the X-axis, the equation will have a negative A value, e.g., y = -A cos(Bx + C) + D.

Front

How do you determine the vertical shift of a sine or cosine graph?

Back

The vertical shift is determined by the value of D in the equation y = A sin(Bx + C) + D or y = A cos(Bx + C) + D.

Front

What is the amplitude of the graph y = 3 sin x?

Back

The amplitude is 3.

Front

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

Back

Changing the value of B affects the period of the graph; the period is calculated as 2π/B.

Front

What does a positive D value indicate in the graph of y = A sin(Bx) + D?

Back

A positive D value indicates a vertical shift upwards.

Front

What is the equation of the graph if it has a vertical shift downwards by 2 units?

Back

The equation would be y = A sin(Bx) - 2 or y = A cos(Bx) - 2.

Front

What is the phase shift of the graph y = sin(x + π/2)?

Back

The phase shift is -π/2, which means the graph shifts to the left by π/2 units.