Graphing Sine & Cosine with Transformations

Front

What is the general form of a cosine function with amplitude and vertical shift?

Back

f(x) = a cos(bx - c) + d, where |a| is the amplitude and d is the vertical shift.

Tags

CCSS.HSF-IF.C.7E

Front

What does the amplitude of a sine or cosine function represent?

Back

The amplitude represents the maximum distance from the midline of the graph to its peak or trough.

Tags

CCSS.HSF-IF.C.7E

Front

How do you determine the period of a cosine function?

Back

The period of a cosine function is given by the formula: Period = (2π)/|b|, where b is the coefficient of x.

Tags

CCSS.HSF.TF.A.4

Front

What is the effect of changing the value of 'b' in the function y = a cos(bx)?

Back

Changing 'b' affects the period of the function; a larger 'b' results in a shorter period.

Tags

CCSS.HSF-IF.C.7E

Front

What is the phase shift in the function y = a sin(bx - c)?

Back

The phase shift is given by c/b, which indicates how much the graph is shifted horizontally.

Tags

CCSS.HSF-IF.C.7E

Front

What is the vertical shift in the function y = a sin(bx) + d?

Back

The vertical shift is represented by 'd' and moves the entire graph up or down.

Tags

CCSS.HSF-IF.C.7E

Front

How do you identify a horizontal shift in the function y = a sin(bx - c) + d?

Back

The horizontal shift is determined by the value of 'c'; if c is positive, the shift is to the right, and if negative, to the left.

Tags

CCSS.HSF-IF.C.7E

Front

What is the amplitude of the function y = 4 cos(x) + 1?

Back

The amplitude is 4, which is the coefficient of the cosine function.

Tags

CCSS.HSF-IF.C.7E

Front

What is the period of the function y = 2 sin(3x)?

Back

The period is (2π)/3, since b = 3.

Tags

CCSS.HSF.TF.A.4

Front

What does a negative amplitude indicate in a cosine function?

Back

A negative amplitude indicates a reflection of the graph across the midline.

Tags

CCSS.HSF-IF.C.7E