Graphing Trig Functions

Front

What is the period of the sine function in the form y = a sin(bx)?

Back

The period is given by the formula \( \frac{2\pi}{|b|} \).

Front

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

Back

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

Front

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

Back

The period is given by the formula \( \frac{2\pi}{|b|} \).

Front

What is a phase shift in trigonometric functions?

Back

A phase shift is a horizontal translation of the graph, determined by the value of c in the function forms \( y = a \sin(b(x - c)) \) or \( y = a \cos(b(x - c)) \).

Front

How do you find the phase shift of the function y = a cos(b(x - c))?

Back

The phase shift is given by \( c \) units to the right if c is positive and \( |c| \) units to the left if c is negative.

Front

What is the amplitude of a trigonometric function?

Back

The amplitude is the maximum distance from the midline of the graph, calculated as \( |a| \) in the functions \( y = a \sin(bx) \) or \( y = a \cos(bx) \).

Front

What does a negative value of a in y = a sin(bx) indicate?

Back

A negative value of a indicates that the graph is reflected over the x-axis.

Front

How does the value of b affect the period of a trigonometric function?

Back

The value of b affects the period by determining how many cycles occur in a given interval; specifically, the period is \( \frac{2\pi}{|b|} \).

Front

What is the effect of a vertical shift on the graph of a trigonometric function?

Back

A vertical shift moves the entire graph up or down without changing its shape.

Front

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

Back

The vertical shift is represented by the value of d; if d is positive, the graph shifts up, and if d is negative, it shifts down.