Precalculus Accelerated
Trig Graphing – 2007
Assign. #20
Name: _____________________________
Today’s preparation determines
tomorrow’s achievements.
Directions: - Write the equation of a secant curve based on the following discription:
1. The corresponding cosine curve has an amplitude of 2 / 3 , a period is ! / 2 , a phase shift to the left of
! / 4 units, and a shift up 3 units.
2. The corresponding cosine curve has an amplitude of 3, a period is 5! , is reflected over the x-axis, and
shifted down 2 units.
Directions - Sketch one cycle of each of the following:
#2
"&
x ! ( +1
4'
$3
3. f (x) = 2csc %
amp: __________
period: ________
phase shift: _______
vertical shift: _______
domain: ___________
range: _________
even/odd/neither?
#"
"&
x + (!2
2'
$3
4. f (x) = ! 3sec %
amp: __________
period: ________
phase shift: _______
vertical shift: _______
domain: ___________
range: _________
even/odd/neither?
( )
5. f (x) = cos 4x over the interval ( ! " , " ).
amp: __________
period: ________
domain: ___________
range: _________
even/odd/neither?
( )
6. f (x) = sin 2x over the interval ( ! " , " ).
amp: __________
period: ________
domain: ___________
range: _________
even/odd/neither?
7. Write the equations of the following curves:
a. _________________________________
!
2!
Answers:
1. f (x) =
2
3
)
6. amp: 1, per: !
3!
7. a. f (x) = 2 csc #
D: ! except x = ...
8
(
right, v.s. 1 up
( !", !1] # [ 3, " )
2
D: ! except x = ...0,3...
( !", !5] # [1, " )
left, v.s. 2 down
[ !1,1]
[ !1,1]
!1 $
x
" 2 &%
b.
8.
3
)
D: !", " , R:
3" 15" 27"
,
,
...
8 8
8
4. amp: 3, per: 6, p.s.
R:
(
D: !", " , R:
%
x' ! 2
&
3. amp: 2, per: 3! , p.s.
R:
2
5. amp: 1, per: ! / 2
sec ( 4x + ! ) + 3
"2
2. f (x) = ! 3 sec $
#5
!
4!
"7
and cos ! < 0 , find tan ! .
25
Given sin ! =
8.
3!
b. __________________________________
7
24
()
f (x) = ! 4 sec x
!
3!
2
2!