Review 2.2
Name:_______________________________
Precalculus
Sinusoidal Functions
y = sin(x)

y = cos(x)
y

y
x








x

 




Domain:
Range:
Range:
Odd/Even/Neither (Circle One)
Odd/Even/Neither (Circle One)
Transformations

Formulas
a:
y = asin(bx - c) + d
b:
y = acos(bx - c) + d
Amplitude:
Period:
c:
Phase Shift:
d:
Interval for One Cycle:
1. Determine the period, amplitude, and phase shift of the sinusoidal functions.

1
x 
4
7


Domain:
a. y  3 cos

b.
3 

y  cos x 

4 

1 
x
3 
c. y  5  2 sin 
d. y 
3
sin(2x   )
4
2. Create a sine equation that has the following transformations and characteristics.
a. Amplitude: 3
Period: π
Phase shift: π/2
b. Amplitude: .5
Period: 2
Phase shift: 0
c. Amplitude: 4
Period : 2π
Phase shift: π/3

3. Determine the period and amplitude of the functions from their graph.
a.
b.
c.
4. Graph the following functions using transformations.
Be sure to Clearly Label Your Axes and your final graph!!!!
a. y = 2 - sin(x)
Amp:
Range:


c. y  1  sin x 
d.
Here’s a few tips for graphing.
 Find your period first!! 2
b
 Then, if you have both “b and c,” find
your endpoints of your period.
 Make sure you know your critical pts and
where they occur.
 Lastly, always reflect/stretch before
you shift up/ down.
b. y = 3cos(x)
Period:
PS:
Amp:
Range:
Period:
PS:
1 
3 

d. y  2cos x 

2

Amp:
Range:
Period:
PS:
Amp:
Range:
Period:
PS:
Other Trigonometric Functions
y = tan(x)

y = cot(x)
y

y
x








x

 






Domain:
Range:
Range:
Odd/Even/Neither (Circle One)
Odd/Even/Neither (Circle One)
y = sec(x)
y = csc(x)
y

y
x





Domain:







x

 







Domain:
Domain:
Range:
Range:
Odd/Even/Neither (Circle One)
Odd/Even/Neither (Circle One)
5 Graph the functions. Describe all of the transformations.
a. f(x) = tan(x) - 2

y








x








b. f(x) = - 12 cot(x)

y





x









c. f(x) = 1- sec(x)

y





x









d. f(x) = 3csc(x +

4
)

y





x









e. f(x) = -2tan(x -

4
)

y








x





