Graphs of Trig Functions

Front

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

Back

The period is given by the formula 2π/B, where B is the coefficient of x.

Front

What is the midline of the cosine function y = a*cos(bx) + d?

Back

The midline is the horizontal line y = d, where d is the vertical shift.

Front

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

Back

The horizontal shift is determined by the value of c.

Front

What does the coefficient 'a' represent in the function y = a*sin(bx) + d?

Back

The coefficient 'a' represents the amplitude of the sine function.

Front

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

Back

The amplitude is 3, which is the absolute value of the coefficient -3.

Front

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

Back

The vertical shift is represented by the value of d.

Front

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

Back

Changing 'b' affects the period of the function; the period is 2π/B.

Front

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

Back

The period is 2π.

Front

How do you re-scale the x-axis for a trigonometric function?

Back

To re-scale the x-axis, take the period and divide it by 4.

Front

What is the general form of a sine function with a phase shift?

Back

The general form is y = a*sin(bx - c) + d.