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.

Tags

CCSS.HSF.TF.A.4

Front

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

Back

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

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

Front

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

Back

The amplitude is 3.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E