Name:
10/13/15
TPC 2
Unit 2
Agenda:
- Warm Up Activity
- finish HW #8 and Review
Homework due Thursday:
PRACTICE FOR QUIZ on GRAPHING
and POW #5 QUIZ! Solutions on website
*UNIT 2 QUIZ 3 AND POW #5 QUIZ Thursday 10/15!!*
!
SOME REVIEW FOR Unit 2 QUIZ #3
on GRAPHING TRANSFORMATIONS of SINE AND COSINE FUNCTIONS
1. FINISH HW #8 (DO PROBLEMS #5 - 8)… writing 4 equations from a graph
2. Graph the following: ! y = 4 sin ( x + 30º )
Amplitude: _________ Vertical Shift: _____________
Range of the function: __________
Horizontal Shift: _____________
Frequency: __________
Period: __________
!
Critical values happen every: _________º The 5 Critical values are: ________________________
3. ! y = − cos(2(x + 2π )) − 3
Amplitude: _________ Vertical Shift: _____________
Range of the function: __________
Horizontal Shift: _____________
Frequency: __________
Period: __________
Critical values happen every: _________ The 5 Critical values are: ________________________
!
⎛π
⎞
4. ! y = 2.5 cos ⎜ (x − 1)⎟ + 4
⎝3
⎠
Amplitude: _________ Vertical Shift: _____________
Range of the function: __________
Critical values happen every:
_________
The 5 Critical values are:
______________________________
Horizontal Shift: _____________
Frequency: __________
Period: __________
π ⎞⎞
⎛1⎛
5. ! y = −0.5sin ⎜ ⎜ x + ⎟ ⎟ + 1.5
⎝4⎝
2⎠⎠
Amplitude: _________ Vertical Shift: _____________
Range of the function: __________
Horizontal Shift: _____________
Frequency: __________
Period: __________
Critical values happen every: _________ The 5 Critical values are: ________________________
!
6. ! y =
(
)
7
cos 5 ( x − 10o ) + 2
2
Amplitude: _________ Vertical Shift: _____________
Range of the function: __________
Horizontal Shift: _____________
Frequency: __________
Period: __________
Critical values happen every: _________º The 5 Critical values are: ________________________
7. Multiple choice. Choose all equations which describe the following graph. You will have
more than one equation circled.
!
y = 3sin(2x)
y = 3sin ( 2 ( x + π ))
5 ⎞⎞
⎛ ⎛
y = −3sin ⎜ 2 ⎜ x − π ⎟ ⎟
⎝
⎝
2 ⎠⎠
⎛1 ⎞
! y = 3sin ⎜ x ⎟
⎝2 ⎠
π ⎞⎞
⎛ ⎛
! y = −3sin ⎜ 2 ⎜ x − ⎟ ⎟
⎝ ⎝
2⎠⎠
! y = 3sin ( 4x )
π ⎞⎞
⎛ ⎛
y = −3cos ⎜ 2 ⎜ x − ⎟ ⎟
⎝
⎝
2⎠⎠
π ⎞⎞
⎛ ⎛
y = −3cos ⎜ 2 ⎜ x + ⎟ ⎟
⎝ ⎝
4⎠⎠
5π ⎞ ⎞
⎛ ⎛
y = 3cos ⎜ 2 ⎜ x −
⎟
⎝
⎝
4 ⎠ ⎟⎠
8. Please write 4 equations for the following trig function.
vertical shift: ______________
amplitude: _________
period: ___________
frequency: _____________
!
For the “+ sin” equation, horiz. shift: _______
y = ___________________
For the “+ cos” equation, horiz. shift: ______
y = ____________________
For the “– sin” equation, horiz. shift: ________
y = ________________________
For the “– cos” equation, horiz. shift: ________
y = ________________________
9. Put in order of least to greatest.
a) cos(1º)
b) cos(–2º)
c) cos(95º)
d) cos (200º)
____________ < ____________ < _____________ < ______________
10. Graph 2 periods of the following function:
! y = 1− 3cos(6(x + 45º ))
Amplitude: _________ Vertical Shift: _____________
Range of the function: __________
Horizontal Shift: _____________
Frequency: __________
Period: __________
Critical values happen every: _________º The 5 Critical values are: ________________________
!
OVER —>
CHALLENGE!!!!!
A sine function has it’s peak at y = 8 and it’s valley at y = -2. It has a period of ! 4π . There is no
horizontal shift. Write its equation.
sketch!
________________________