Precalculus - Accelerated
Trig Graphing – 2007
Assign. #22
Directions - Graph one cycle of each (two cycles for tan x and cot x):
1. y = ! 2sin ( ! x ) + 2
amplitude: _____________
period: ________________
phase shift:_____________
vertical shift: ___________
Domain: _______________
Range: ________________
Odd, even, or neither?
"
2. y = 2 tan(x ! )
3
amplitude: _____________
period: ________________
phase shift:_____________
vertical shift: ___________
Domain: _______________
Range: ________________
Odd, even, or neither?
3. y = cot (2x + ! )
amplitude: _____________
period: ________________
phase shift:_____________
vertical shift: ___________
Domain: _______________
Range: ________________
Odd, even, or neither?
4. y = sec( 4x ! " ) + 1
amplitude: _____________
period: ________________
phase shift:_____________
vertical shift: ___________
Domain: _______________
Range: ________________
Odd, even, or neither?
Name: _____________________
Today’s preparation determines
tomorrow’s achievements.
Directions - Graph the following over the interval #$ !" , " %& .
5.
"1 %
y = ! 3csc $ x '
#2 &
amplitude: _____________
period: ________________
phase shift:_____________
vertical shift: ___________
Domain: _______________
Range: ________________
Odd, even, or neither?
1
6. y = cos !2x ! "
3
(
)
amplitude: _____________
period: ________________
phase shift:_____________
vertical shift: ___________
Domain: _______________
Range: ________________
Odd, even, or neither?
! x$
7. y = tan # &
" 2%
amplitude: _____________
period: ________________
phase shift:_____________
vertical shift: ___________
Domain: _______________
Range: ________________
Odd, even, or neither?
Directions - Write the secant and the cosecant equation for the graph below.
8.
sec eq: ___________________________
csc eq:___________________________
2
2
! 2! ! 4! 5! 2!
3 3
3 3
9. You are riding your bike down a gravel road when a nail gets stuck in your bike tire. The tire is 28 inches in
diameter and the tire completes one rotation every 1 second. Write a sine and a cosine equation for the
height the nail is above the ground with respect to time.
10. Write the equation of the cotangent curve having a period of 2π and a shift left
11. Write the tangent equation for the
"
"
3!
4
!
2
"
!
4
12. Evaluate:
)"
*#
log 6 + $ tan
graph below.
!
4
!
2
!
3!
4
!
.
2
" 5! % % ,
10! % "
13!
11!
•
csc
( ' ' . + sec
• cos
'
$
$
# 4 && 3 & #
6
6
Answers:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
1. neither
5. odd
3
2!
3!
2
!
!
2
"
!"
3
2. neither
6. even
!
!"
π
3
5π
6
11π
6
4π
3
ps.:
!
2
!
3"
4
!
2
r:
left
d: ! except x = ... !
r: ( !", " )
Odd
" "
, 0, ...
2
2
!
4
#
9. y = 14sin % 2! x "
$
2
vs: 1 up
(
] [ )
(
)
1 &
! + 14,
2 ('
y = !14cos 2" x + 14
right
r: !",0 # 2, "
neither
( !"," )
#3
"3 %
"&
y = sec % x ! ( ! 1 or y = ! csc $ x ' ! 1
2'
$2
#2 &
!
d: ! except x = ...
3"
4
8. answers vary:
4. amp: none
ps.:
"
4
"
4
Odd
vs: none
period:
!
"
7. amp: none
period: 2!
ps.: none
vs: none
d: ! except x = ... ! 3" , !" , " ...
3. amp: none
period:
7π
3
"
2
"
2
3! 5!
8
,
8
...
"1
!%
x+ '
4&
#2
10. y = cot $
#
11. y = ! tan % 2x !
$
12.
3
2
"&
2 ('