Sine and Cosine Graphs

Front

What is the period of the function y = a cos(bx)?

Back

The period is given by the formula: Period = 360° / |b|.

Front

What is the amplitude of the function y = a sin(bx)?

Back

The amplitude is the absolute value of 'a' in the function, which represents the maximum distance from the midline.

Front

How do you determine the vertical shift of a cosine function?

Back

The vertical shift is determined by the constant added or subtracted from the function, represented as y = a cos(bx) + d, where d is the vertical shift.

Front

What does a phase shift refer to in trigonometric functions?

Back

A phase shift refers to the horizontal shift of the graph, which can be left or right, determined by the value of c in y = a cos(b(x - c)).

Front

What is the period of the function y = 4cos(5x)?

Back

The period is 72 degrees.

Front

What is the vertical shift of the function y = 4cos(0.5x + π) - 2?

Back

The vertical shift is down 2 units.

Front

What is the period of the sine and cosine functions y = sin(x) and y = cos(x)?

Back

The period is 360 degrees.

Front

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

Back

The amplitude is 3.

Front

How does the value of 'b' in y = a sin(bx) affect the graph?

Back

The value of 'b' affects the period of the function; specifically, the period is 360° / |b|.

Front

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

Back

A negative 'a' value reflects the graph across the x-axis.