1. Developing
Expert
Voices
1

2. Produced By ;
Sergio
&
Wendy
2

3. Inspiration
Test On Transformation
:
Unit Circular Functions
3

4. 1. The average monthly maximum temperature in Winnipeg, Manitoba has it's
lowest temperature of ­12ºC in January, and a highest temperature of 26ºC in
July.
a) Sketch the graph and give 2 equations, a sine and a cosine
function.
b) what is the maximum temperature for June?
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5. a) Sketch the graph and give 2 equations, a sine and a cosine
function.
We start graphing by labeling our x­axis and y­axis.
y
x
­x
­y
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6. We then plot our known maximum and minimum points.
Also, we label the x­axis in months beginning with they're first letter of the
month.
y
26ºC
­x x
FM A M J J S O N DJ
A
­12ºC
­y
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7. From these two points we can solve for D and A in our equation. ­12 + 19 = 7
December is solved by calculating half of the distance between the
maximum and minimum.
_ = 19
38
26ºC + (­12ºC) =
2
( Dividing by 2 because to
7ºC solve for D we would solve
it by calculating half the
x ­x distance between the
MJJ
FM A S O ND
A J maximum and minimum.)
We then place our sinusoidal axis at 7ºC and 7 also
becomes our quot;Dquot; (December)
A is the amplitude, it's the distance from sinusodal
axis to the maximum or minimum, which in that
case is 19. Therefore, our quot;Aquot; is 19.
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8. B can be solved by taking 2π divided by the
period. The Period is the time it takes the
function to complete a full wave. In this case, a
_
full wave takes place in 12 months so B = 2π
7ºC
12
x ­x
MJJ
FM A S
A J
O ND
In a cosine graph, the function
starts at it's maximum. For this
particular graph to start at it's
maximum, it has to be moved 6
units to the right because the
equation has (x­c), the value of C
has to be the opposite sign.
therefore C = 6
We now have out cosine equation :
_ (x+6) + 7
y = 19cos 2π
12
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9. The sine graph is the same except for the value of
C. A sine graph starts at the sinusoidal axis. The
graph has to be shifted 3 units to the right,
opposite sign, C = 3.
We now have out sine equation :
_ (x­3) + 7
y = 19sin 2π
12
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10. b) what is the maximum temperature for June?
To find the maximum temperature for June, we use one of the
equations. we already know the value of x because January = 0
and June = 5. We substitute 5 into the equation for x and the y
value will give us the average temperature for June.
_
y = 19cos 2π (x ­ 6) + 7
12
_
y = 19cos 2π (5 ­ 6) + 7
12
y = 19cos (­0.5235987756) + 7
y = 19(0.8660254038) + 7
y = 23.45ºC
Therefor the average temperature for June is 23.45ºC
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11. Another way to solve this problem is to use the sin equation,
which will give us the same final answer but from a different
solution to get there.
_
y = 19cos 2π (x ­ 3) + 7
12
_
2π (5 ­ 3) + 7
y = 19cos
12
y = 19sin(1.047197551) + 7
y = 19(0.8660254038) + 7
y = 23.45ºC
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12. Attachments
10x10.gif
GraphP1.gif
GraphP2.gif
quadone.gif