Properties
Transformations
What's my equation?
Word Problems
True or False
100
The domain of sine function
What is xER (all real numbers)?
100
The horizontal and vertical shift of the function below.
y=-5sin(x-45)+2
What is shifted right 45 and up 2
100
The a-value when a function has a max of 6 and a min of -6.
What is a = 6
100
What is the amplitude, domain, and range for:
f(x) = sin x + 3
a = 1
D:{XER}
R:{YER|2<y<4}
100
(True or False) This represents a periodic function:
True
200
What two letters of sine function work together to tell you the range?
What is a and c?
200
The horizontal and vertical shift of the function below.
y=4sin(x+90)-2
What is shifted left 90 and down 2
200
The equation for a Sine Function with an amplitude of 2 and has a vertical shift of -5.
What is: y = 2 sinx - 5
200
Why can the movement of the hands on a clock be represented by a Sine Function?
Because the position of the hands have consistent repeating values
200
(True or False) The c-value for this graph is c = 1
False (c = 0)
300
What is the range of a sine function with a=1 and c=0
What is {yER -1 <y<1}
300
What transformations have been applied?
y=-sin(x-30)+6
reflected down
shifted right 30
shifted up 6
300
The c-value of this graph
What is c = 2?
300
What are three things in our everyday life that can be represented by a Sine Function?
Ferris Wheel, tides, phases of the moon, sunrise/sunset, windmill blades, waterwheel...
300
(T/F): A positive a-value has a graph of sine function that reflects about the x-axis.
False
400
The definition of the period of a periodic function
What is the horizontal distance on the graph when the patter repeats itself?
400
What transformations have been applied?
y=1/2 sinx+1
vertical compression by 1/2
a = 1/2
shifted up 1
400
The amplitude of this graph
What is a = 3?
400
The spokes of a water wheel go around in a consistent pattern, represented by:
h(x)=sin x
What is the radius of the water wheel?
radius = 1
400
T/F: These are co-terminal angles: 75 & 425
False
500
For the general function in the form given below. This is the explanation for what causes a phase shift left or right.
y = a sin[k(x - d) + c
What is -d is a phase shift left (x + d)
and
+d is a phase shift right (x - d)
500
What transformations have been applied?
y= 4sin(5(x-10))+7
vertically stretched by 4, a = 4
period = 72 (horizontally compressed)
shifted right 10
shifted up 7
500
The Sine Function equation, when the function has a period of 90 and a phase shift of right 45.
What is: y = sin[4(x - 45)]
500
The height of a Ferris Wheel is modelled by:
h(x)=6sin(x-45)+7
What are the maximum and minimum heights of the riders on the Ferris Wheel?
max = 13
min = 1
500
T/F: The period is 4
True