Graphing Trig Functions

Front

What is the amplitude of a cosine function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak. For the function y = A cos(Bx + C) + D, the amplitude is |A|.

Front

What is the equation of a cosine function with an amplitude of 5?

Back

y = 5 cos(x) or y = 5 cos(5x) (the amplitude is determined by the coefficient before the cosine).

Front

What is the range of the function y = A cos(Bx) + D?

Back

The range is given by [D - |A|, D + |A|]. For example, if A = 2 and D = 0, the range is [-2, 2].

Front

What does vertical shift mean in a trigonometric function?

Back

Vertical shift refers to the movement of the graph up or down. It is determined by the value of D in the function y = A cos(Bx) + D.

Front

What is the amplitude for the function y = 4cos(1/2 x + π) - 2?

Back

The amplitude is 4.

Front

What is the vertical shift for the function y = 4cos(1/2 x + π) - 2?

Back

The vertical shift is Down 2.

Front

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

Back

The period is given by the formula P = 2π/|B|. For example, if B = 2, the period is π.

Front

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

Back

The amplitude is 3 (the negative sign indicates a reflection, but amplitude is always positive).

Front

What is the equation of a cosine function with a vertical shift of 3?

Back

y = A cos(Bx) + 3, where A is the amplitude and B affects the period.

Front

What is the range of the function y = 3cos(x) + 1?

Back

The range is [-2, 4]. (Calculated as [1 - 3, 1 + 3]).