Sunrise Question
Upcoming SlideShare
Loading in...5
×
 

Sunrise Question

on

  • 3,314 views

 

Statistics

Views

Total Views
3,314
Slideshare-icon Views on SlideShare
3,287
Embed Views
27

Actions

Likes
0
Downloads
1
Comments
0

3 Embeds 27

http://strawberryshortcakeforever.blogspot.com 23
http://www.slideshare.net 3
http://strawberryshortcakeforever.blogspot.ca 1

Accessibility

Categories

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

    Sunrise Question Sunrise Question Presentation Transcript

    • The Sunrise Question
    • with solutions…
    • THE QUESTION [info]:
      • The latest sunrise in Montreal was on Dec. 22 at 9:15 AM . According to the almanac, the earliest sunrise occurred on the 22nd of June at 3:15 AM . The sunrise times on other dates can be predicted using a sinusoidal equation.
      • **Assume there is no daylight savings time in Montreal.**
    • THE QUESTION: Part I
      • (a) Write two equations for the described function above; one using cosine and the other using sine.
    • THE SOLUTION: Part I
      • STEPS
      • PROCESS
      • Read the given info and convert it into information that can be used in an equation. For example, the time is not going to be written 9:15 on the graph but 9.25 because 15 min. is a quarter of an hour.
      • Make two lists for the parameters A, B, C & D. One set will be used for the cosine equation and the other will be used for the sine equation.
      • Find the parameters in the mean of DABC [stretches before translations]. To find parameter D, add the min. and max. value and then divide by 2 to find the sinusoidal axis .
      • To find parameter A, subtract the average value from the maximum value to get A.
      cont‘d on the next slide; Hupsha, hupsha now…
      • STEPS
      • PROCESS
      • cont’d...
      • Parameter B is equal to 2 π divided by the period, which happens to be the number of days in a year; 364.
      • The phase shift (C) is found depending on what kind of equation is being used. If the cosine equation is being found, the maximum value is usually on the y-axis. But the information tells us that the maximum value occurs on Dec. 22, 9 days before Jan. 1 [the y-axis].
      • The phase shift in the sine equation is determined by finding out the distance of the average value to the y-axis.
      • Finally, to get the equations, plug in the values found into the general formula.
    • THE QUESTION: Part II
      • (b) Sketch the graph for the sinusoidal function described in the problem.
    • THE SOLUTION: Part II
      • STEPS
      • Acknowledge that Dec. 22 is 9 days before Jan. 1. [use this later in graphing stage.]
      • To find the values within the period of one cycle in the graph, subtract nine days from the full, half, and quarter periods.
      • On the y-axis, label where the min. value, max. value and sinusoidal axis are. Plot the points according to info; max value at Dec. 22.
      • Label the axes.
    • THE GRAPH…
    • THE QUESTION: Part III
      • (c) Use one of the equations in (a) to predict the time of sunrise on September 7.
    • THE SOLUTION: Part III
      • Find out what the day of the year September 7 th is by adding up the total number of days in each month up to the given date, assuming there is no daylight savings time.
      • Since d lies along the x-axis, treat the number of days as an x-coordinate and plug in as d in the formula, either sine or cosine and solve.
      • Sun, sun...Mr. Golden Sun.
    • THE QUESTION: Part IV
      • (d) What is the average sunrise time throughout the year?
    • THE SOLUTION: Part IV
      • STEPS
      • PROCESS
      • The avg. sunrise time equals the sinusoidal axis. To find this, find parameter D by adding the minimum and maximum value and divide by two.
    • Looking at the sun gives me a feeling of freedom. Too bad Max can’t feel this way…
      • Sunrise Over Rocks, Lighthouse Beach by flickr user Captain Capture