Sin Cos Graphs - Rochester City School District / Overview
[Pages:4]Pre-Calculus 1.5 Graphs of Sine and Cosine Functions Assignment #44
Name____________________________ Period____________ Group #________
Determine the amplitude and period of each function.
1.
y = sin 4x
Amplitude = _________
Period = ____________
2.
y = cos 5x
Amplitude = _________
Period=_____________
3.
y = sin x
Amplitude=___________
Period=______________
4.
y = 4 cos x
Amplitude = _________
Period = ____________
5.
y = ?2 sin x
Amplitude = _________
Period=_____________
6.
y = 2 sin (?4x)
Amplitude=___________
Period=______________
7.
y = 3 sin 2 x
3
Amplitude = _________
Period = ____________
8.
y = ?4 cos 5x
Amplitude = _________
Period=_____________
9.
y = 3 cos (?2x)
Amplitude=___________
Period=______________
Give the amplitude and period of each function graphed below. Then write an equation of each graph.
10. 3
11. 4
?
?2
2
?4
?2
2
4
?3 Amplitude = _________ Period = ____________ Equation: ___________ 12.
2
?4 ?2
2
4
?2
Amplitude = _________ Period = ____________ Equation: ___________
?4
Amplitude=___________ Period=______________ Equation:____________ 13.
5
?2 ?
2
?5 Amplitude=___________ Period=______________ Equation:____________
Give the amplitude and period of each function. Then sketch the graph of the function over the interval ? 2 x 2 using the key points for each function.
14. y = 3 sin x
15. y = 2 cos x
Amplitude = _________ Period = ____________
16. y = 3 sin 2x
Amplitude=___________ Period=______________
17. y = 4 cos 2x
Amplitude = _________ Period = ____________
Amplitude=___________ Period=______________
18.
y = 3 cos 1 x
2
19. y = cos(?3x)
Amplitude = _________ Period = ____________
20. y = ?2 sin(?2x)
Amplitude=___________ Period=______________
Amplitude = _________ Period = ____________ 21. Find an equation for a sine function that has amplitude of 4, a period of .
22.
Find an equation for a cosine function that has an amplitude of
3 5
,
a
period
of
3 2
.
23. Find an equation for a sine function that has amplitude of 5, a period of 3.
HOW OFTEN DID THE STUDENT WHO GOT "C" ON HIS TRIG FUNCTIONS TEST DO HIS HOMEWORK?
f(x) = Asin(Bx) f(x) = Acos(Bx)
|A| = Amplitude B represents the number of complete waves in an interval of 2, therefore 2 = Period
B
1) f (x ) 2sinx
2) f (x ) sin(2x )
3) f (x ) sin x 4
4)
f
(x
)
cos
1 2
x
5) f (x ) cos(3x )
6) f (x ) 1 sin(3x ) 2
9)
f
(x )
3 2
sin
1x 2
10) f (x ) 4cos(x )
7) f (x ) 3sin(2x ) 8) f (x ) 4sinx
11)f (x ) 3sin x 3
12)f (x ) 2cos(3x )
Match each function from above with a graph below.
A.
C.
D.
E.
I.
I.
L.
L.
O.
P.
R.
Y.
8 2 11 3 5 1 7 4 9 12 6 10
................
................
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