Unit 2: Trig Graphs

Front

What is a phase shift in trigonometric functions?

Back

A phase shift is a horizontal shift left or right for periodic functions, determined by the value of 'c' in the equation of the form y = a sin(b(x - c)) + d.

Front

How do you determine the phase shift from the equation y = a sin(b(x - c)) + d?

Back

The phase shift is given by the value of 'c' in the equation, calculated as c/b.

Front

What is a vertical shift in trigonometric functions?

Back

A vertical shift is a movement up or down for periodic functions, determined by the value of 'd' in the equation of the form y = a sin(b(x - c)) + d.

Front

How do you identify the vertical shift in the equation y = a sin(b(x - c)) + d?

Back

The vertical shift is represented by the value of 'd' in the equation.

Front

What is the amplitude of a trigonometric function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak, calculated as |a| in the equation y = a sin(b(x - c)) + d.

Front

How do you find the period of a trigonometric function?

Back

The period is calculated as 2π/|b|, where 'b' is the coefficient of x in the equation y = a sin(b(x - c)) + d.

Front

What is the equation of a sine function with a phase shift of 1?

Back

The equation can be expressed as y = a sin(b(x - 1)) + d.

Front

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

Back

The equation can be expressed as y = a cos(bx) + π.

Front

How does changing the value of 'a' affect the graph of a trigonometric function?

Back

Changing 'a' affects the amplitude of the graph; a larger |a| results in a taller graph, while a smaller |a| results in a shorter graph.

Front

What is the significance of the value 'b' in the equation of a trigonometric function?

Back

The value 'b' affects the period of the function; specifically, the period is 2π/|b|.