Trig Graph Review

y-intercept of the tangent function

(0,0)

Amplitude or vertical stretch factor

Half the difference between the maximum and minimum y-values of the graph of a sine or cosine function is called the ??? of the graph or wave.

Where are the x-intercepts (zeros) of y = cos 4pi

x-intercepts (zeros) are at pi/8 and 3pi/8

domain of cosine function

(-∞,∞)

Relationship between sin and arcsin

Inverse Functions

Relationship between sin and csc

Reciprocal Functions

x=π/2 and x = -π/2

The asymptotes of f(x) = tan x

Period

The horizontal length of one cycle.

π

The period for tangent is ?? and not the same as it was for the sine and cosine functions.

2π/|b|

To determine the Period of Cosine and Sine functions

range of sine function

[-1,1]

Identify the transformations in the graph: y = 2 sin x/2

amplitude = 2 period = 4pi

Identify the transformations in the graph: y = 2 sin (x/3 - 3pi/4) - 2

amplitude = 2 period = 6pi phase shift to the right 9pi/4 radians vertical shift down 2 unit

Identify the transformations in the graph: y = 2 sin (4x + pi/6) - 2

amplitude = 2 period = pi/2 phase shift to the left pi/24 radians vertical shift down 2 units

Identify the transformations in the graph: y = 2 tan (2x - pi/3) + 2

amplitude = 2 period = pi/2 phase shift to the right pi/6 vertical shift up 2

What is the domain and range of y = 2 cos (pi/2 + 5pi/4) + 1

domain: all real numbers range: [-1, 3]

What is the domain and range of y = -1 + 4 cos (3x - pi/6)

domain: all real numbers range: [-5, 3]

vertical shift

is a translation of a geometric object in a direction parallel to the vertical axis (y-axis)

Identify the transformations in the graph: y = cos (3x + pi/3)

period = 2pi/3 phase shift to the left pi/9 radians

Identify the transformations in the graph: y = 2 sin (3x + pi/3) - 2

vertical shift down 2 units amplitude = 2 period = 2pi / 3 phase shift to the left pi/9

Where are the x-intercepts (zeros) of y = 4 sin (x/2)

x-intercepts (zeros) are at 0, 2pi, 4pi

domain of the tangent function

All angles x except odd integrals of π/2

Identify the transformations in the graph: y = 3 cos (x/4 - 5pi/6) - 2

amplitude = 3 period = 8pi phase shift to the right 10pi/3 radians vertical shift down 2 unit

Identify the transformations in the graph: y = 3 tan (2x + pi/4) - 2

amplitude = 3 period = pi/2 phase shift to the left pi/8 radians vertical shift down 2 unit

Identify the transformations in the graph: y = 3 sin (4x - pi/4) - 1

amplitude = 3 period = pi/2 phase shift to the right pi/16 radians vertical shift down 1 unit

Identify the transformations in the graph: y = 3 sin 4x - 1

amplitude = 3 period = pi/2 vertical shift down 1 unit

Identify the transformations in the graph: y = 4 tan (x/2 + pi/2) + 2

amplitude = 4 period = 4pi phase shift to the left pi radians vertical shift up 2 units

Identify the transformations in the graph: y = 4 cos (x/4 + 3pi/4) - 2

amplitude = 4 period = 8pi phase shift to the left 3pi radians vertical shift down 2 unit

y= a sin b(x - c) + d

graphing form of sine.