TRIGONOMETRY
1. Graph
graphing
trig functions
math
hands
CH 03 SEC 03 SOLUTIONS
y = sin x
note changes on eq. and on graph
graph
y = sin(−x)
replace
3
2
1
0 ◦
0
-1
-2
-3
90◦
new eq.
180◦ 270◦ 360◦
3
2
1
0 ◦
0
-1
-2
-3
90◦
180◦ 270◦ 360◦
on graph
Solution:
y = sin x
3
2
1
0 ◦
0
-1
-2
-3
y = sin x
90◦
2. Graph
180◦ 270◦ 360◦
y = sin x
replace x 7→ −1x
x
on graph
mult ALL
x’s
1/-1
3
2
1
0 ◦
0
-1
-2
-3
note changes on eq. and on graph
y = sin(−1x)
90◦
graph
180◦ 270◦ 360◦
−2y = sin(x)
replace
3
2
1
0 ◦
0
-1
-2
-3
90◦
180◦ 270◦ 360◦
new eq.
3
2
1
0 ◦
0
-1
-2
-3
90◦
180◦ 270◦ 360◦
on graph
Solution:
pg. 1
c
2007-2011
MathHands.com v.1012
TRIGONOMETRY
y = sin x
3
2
1
0 ◦
0
-1
-2
-3
y = sin x
90
3. Graph
◦
180
◦
graphing
trig functions
math
hands
CH 03 SEC 03 SOLUTIONS
270
◦
360
replace
y
7→
−2y
x
on
graph
mult
ALL
y’s 1/2
◦
y = cos x
3
2
1
0 ◦
0
-1
-2
-3
note changes on eq. and on graph
−2y = sin(x)
90◦
graph
180◦ 270◦ 360◦
y = cos(−x)
replace
3
2
1
0 ◦
0
-1
-2
-3
90◦
new eq.
180◦ 270◦ 360◦
3
2
1
0 ◦
0
-1
-2
-3
90◦
180◦ 270◦ 360◦
on graph
Solution:
3
2
1
0 ◦
0
-1
-2
-3
4. Graph
pg. 2
y = cos x
y = cos x
90◦
180◦ 270◦ 360◦
y = cos x
replace x 7→ −1x
x
on graph
mult ALL
x’s
1/-1
note changes on eq. and on graph
3
2
1
0 ◦
0
-1
-2
-3
y = cos(−1x)
90◦
graph
180◦ 270◦ 360◦
−.5y = cos(x)
c
2007-2011
MathHands.com v.1012
TRIGONOMETRY
graphing
trig functions
math
hands
CH 03 SEC 03 SOLUTIONS
replace
3
2
1
0 ◦
0
-1
-2
-3
90◦
new eq.
180◦ 270◦ 360◦
3
2
1
0 ◦
0
-1
-2
-3
90◦
180◦ 270◦ 360◦
on graph
Solution:
y = cos x
3
2
1
0 ◦
0
-1
-2
-3
y = cos x
90◦
5. Graph
180◦ 270◦ 360◦
y = sin x
replace
y
7→
−.5y
x
on
graph
mult
ALL
y’s 1/.5
3
2
1
0 ◦
0
-1
-2
-3
note changes on eq. and on graph
−.5y = cos(x)
90◦
graph
180◦ 270◦ 360◦
−.5y = sin(x)
replace
3
2
1
0 ◦
0
-1
-2
-3
90◦
180◦ 270◦ 360◦
new eq.
3
2
1
0 ◦
0
-1
-2
-3
90◦
180◦ 270◦ 360◦
on graph
Solution:
pg. 3
c
2007-2011
MathHands.com v.1012
TRIGONOMETRY
y = sin x
3
2
1
0 ◦
0
-1
-2
-3
y = sin x
90
6. Graph
◦
180
◦
270
graphing
trig functions
math
hands
CH 03 SEC 03 SOLUTIONS
◦
360
replace
y
7→
−.5y
x
on
graph
mult
ALL
y’s 1/.5
◦
y = sin x
3
2
1
0 ◦
0
-1
-2
-3
note changes on eq. and on graph
−.5y = sin(x)
90◦
graph
180◦ 270◦ 360◦
−.5y = sin(4x)
replace
3
2
1
0 ◦
0
-1
-2
-3
90◦
new eq.
180◦ 270◦ 360◦
3
2
1
0 ◦
0
-1
-2
-3
90◦
180◦ 270◦ 360◦
on graph
Solution:
3
2
1
0 ◦
0
-1
-2
-3
7. Graph
pg. 4
y = sin x
90◦
180◦ 270◦ 360◦
y = sin x
y = sin x
7
4x
replace x →
y
7→
−.5y
x
on graph
mult ALL
y’s
1/-.5
mult
ALL
x’s
1/4
note changes on eq. and on graph
3
2
1
0 ◦
0
-1
-2
-3
−.5y = sin(4x)
90◦
180◦ 270◦ 360◦
graph
−.5y = sin(−4x)
c
2007-2011
MathHands.com v.1012
TRIGONOMETRY
graphing
trig functions
math
hands
CH 03 SEC 03 SOLUTIONS
replace
3
2
1
0 ◦
0
-1
-2
-3
90◦
180◦ 270◦ 360◦
new eq.
3
2
1
0 ◦
0
-1
-2
-3
90◦
180◦ 270◦ 360◦
on graph
Solution:
3
2
1
0 ◦
0
-1
-2
-3
pg. 5
y = sin x
90◦
180◦ 270◦ 360◦
y = sin x
replace x 7→ −4x
y
7→
−.5y
x
on graph
mult ALL
y’s
1/-.5
mult
ALL
x’s
1/-4
3
2
1
0 ◦
0
-1
-2
-3
−.5y = sin(−4x)
90◦
180◦ 270◦ 360◦
c
2007-2011
MathHands.com v.1012