1.
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Remember folks: You are all born on Pi day!
NOW THE GOOD STUFF.Mr. K’s Example:
For a Saskatchewan town the latest sunrise is on Dec 21 at 9:15am. The earliest sunrise is on June 21 at 3:15am. Sunrise times on other dates can be predicted using a sinusoidal equation. Note: There is no daylight savings time in Saskatchewan.
a) Sketch the graph of the sinusoidal function described.
b) Write 2 equations for the function one using sine the other cosine.
c) Use one of the equations in (b) to predict the time of sunrise on April 6.
d) What is the average sunrise time through the year?
e) On what days will the sun rise at 7:00am?
In order for us to solve this equation, we need to visualize it. So let’s make a graph! And pictures are always prettier =]
a) Sketch the graph of the sinusoidal function described.
March10 01
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(to view properly, please enlarge! ohh and please ignor my spelling......... and grammar.......)
(to view properly, please enlarge! ohh and please ignor my spelling......... and grammar.......)
b) Write 2 equations for the function one using sine the other cosine.
Sine |
| | Cosine | |
A= |
| -3 | A= | +3 |
B= |
| 2pi/364 | B= | 2pi/364 |
C= |
| +81 | C= | -10 |
D= |
| 6.25 | D= | 6.25 |
Using f(x) = A sin B ( x - C ) + D we end up with:
- f(x) = -3 sin [ 2pi / 364 ( x - 81 ) ] + 6.25
and g(x) = A cos B ( x - C ) + D we get:
- g(x) = 3 cos [ 2 pi / 364 ( x + 10 ) ] + 6.25
(I'm not sure how to explain this part. I'm hoping this is pretty much straight foward for everybody...... If not, just comment and I'll atempt to explain it.)
c) Use one of the equations in (b) to predict the time of sunrise on April 6.
To find the the time of sunrise of April 6, we need to find what day that is.
(Month vs # of days)
January 31, February 28, March 31, April 6
31 + 28 + 31 + 6 = 96
Now replace the x with 96.
- f(96) = -3 sin [ 2pi / 364 ( 96 - 81 ) ] + 6.25
or
- g(96) = 3 cos [ 2 pi / 364 ( 96 + 10 ) ] + 6.25
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nice job emme, even though it took a long time you did well :P
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