Math Apps 12. Sinusoidal Functions. Third Assignment
1.
Describe how the given functions differ from y = sin(x)
(For example: shifted up by 7, period is half the length)
a) y = 5 sin (x) + 2
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b) y = sin (3x) – 4
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c) y = 2sin(x – 3)
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d) y = 1.2sin (πx +π) – 1
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2. For each graph fill in the table.
a)
b)
Amp
Period
Amp
Period
Horiz Shft
Verti Shft
Horiz Shft
Verti Shft
3.
Determine the equation of a sine function have the indicated amplitude, period, and phase
shifts.
a) Amplitude is 5, vertical shift is – 1, horizontal shift is 2.
b) Period is π, vertical shift is 3.
c) Amplitude is 0.5, period is 4π, horizontal shift is π.
4. For the following equations determine the value. All x values are in radians unless otherwise
specified.
y = sin(x) find y if,
a) x = π
b) x = 135°
c) x = 1.7
d) x = – 2.53
y = 3sin(2x – 4 ) + 1 find y if,
a) x = π
b) x = 1.7
c) x = – 2.53
y = -2sin(4x + 320°) – 7 find y if,
a) x = 90°
b) x = 135°
c) x = 57°
d) x = – 117°
5. For the following graphs determine the corresponding y and x values for the values given
a) x = 2, y =
b)
x = 5, y =
_____
_____
c) Y = -1, x = ________________
d) Y = -3, x = ________________
a) x = 0, y = ________
b) x = 3.7, y = ______
c) y = 2 , x = ______________
d) y = 1.2, x = ____________
a) x = 5, y = ______
b) x = 3.25, y = ______
c) y = 0.3 , x = _________
6. For the following equations determine the value. All x values are in radians unless otherwise
specified.
y = sin(x) find all x’s where x is between zero and two pi ( 0 ≤ x <2π )
a) y = 1
b) y = 0
c) y = 0.866
d) x = -0.4
y = 3sin(x + π/2 ) + 1 find all x’s where x is between zero and two pi ( 0 ≤ x <2π )
a) y = 4
b) y = -2
c) y = 0
y = -2sin(4x ) find all x’s where x is between zero and half pi ( 0 ≤ x <π/2 )
a) y = 1
b) y = - 0.5
c) y = 1.6
d) y = 8