Graphing Trig Functions

Find the amplitude and period of the function: y=-3/2cos(2πx)

Give the exact values, not decimal approximations.

Amplitude=3/2

Period=1

Find the phase shift, period, and amplitude of the function: y=-cos(2πx+π)-1
Give the exact values, not decimal approximations.

Phase Shift=-1/2

• (because a cos(b(x-c/b))+d where “-c” is “-π” and “b” is “2π.” Do -π/2π=-1/2”)

Period=1 (because “2π/2π=1”)π

Amplitude=1

Find the amplitude, phase shift, and period of the function: y=-2+4sin(2x-π/3)
Give the exact values, not decimal approximations.

Phase Shift=π/6

Period=π

Amplitude=4

What are the domains and ranges of the following functions?
1.) y=cotx

Domain:

Range:

2.) y=cosx

Domain:

Range:

3.) y=secx

Domain

Range:

1.) y=cotx

Domain:The set of all real numbers, except integer multiples of π

Range: The set of all real numbers

2.) y=cosx

Domain: The set of all real numbers

Range: The set of all real numbers from -1 to 1

3.) y=secx

Domain: The set of all real numbers, except odd integer multiples of π/2

Range: The set of all real numbers less than or equal to -1 or greater than or equal to 1

—-

4.) y=sinx

Domain: The set of all real numbers

Range: The set of all real numbers from -1 to 1

5.) y=cscx

Domain: The set of all real numbers, except integer multiples of π

Range: The set of all real numbers less than or equal to -1 or greater than or equal to 1

6.) y=tanx

Domain: The set of all real numbers, except odd integer multiples of π/2

Range: The set of all real numbers

Graph the trigonometric function: y=-3/2sinx

Plot all points corresponding to -intercepts, minima, and maxima within one cycle. Then click on the graph-a-function button.

Graph the trigonometric function: y=sin(3/2x)

Plot all points corresponding to -intercepts, minima, and maxima within one cycle. Then click on the graph-a-function button.

Graph the trigonometric function: y=sinx-3 Plot all points corresponding to minima and maxima within one cycle. Within that cycle, also plot all points along the "midline" (points whose -coordinates are midway between the function's minimum and maximum values). Then click on the graph-a-function button.

Graph the trigonometric function:

y=sin(x-7π/6)

Plot all points corresponding to -intercepts, minima, and maxima within one cycle. Then click on the graph-a-function button.

Graph the trigonometric function:

y=5/2sin(x+π/4)

Plot all points corresponding to -intercepts, minima, and maxima within one cycle. Then click on the graph-a-function button.

Graph the trigonometric function:

y= 5/2cos(1/2x)

Plot all points corresponding to -intercepts, minima, and maxima within one cycle. Then click on the graph-a-function button.