Performance+Task+1

__**Introduction to Analytic Trigonometry**__ Source: > PRECALCULUS: 4th Edition > Larson Hostetler >
 * Chapter 5: Analytic Trigonometry

Students are to consider the following prompt:

The number of hours of daylight that occur at any location on earth depends on two things: the time of the year and the latitude of the location. Here are models for the number of hours of daylight in Seward, Alaska (60 degrees latitude) and New Orleans, Louisiana (30 degrees latitude).

Seward D=12.2 – 6.4cos[ p (t + 0.2)/6] New Orleans D=12.2– 1.9cos[ p (t + 0.2)/6]

In these models, D represents the number of hours of daylight and t represents the month, with t=0 representing January 1. Analyze both of the equations and take notice to the trigonometric function used (cosine). Consider the graph of the cosine function. We will be working a lot with this and the other trig functions in chapter five. The goal of the assignment is to become comfortable with graphing and analyzing equations, especially ones using trig identities. Things to include: (1) Graph both equations on the same xy plane. Be sure your graph is easy to read and labeled properly. Graphs can be created by hand or in excel but use a graphing calculator to aid. Be neat. (2) Are there any critical values for either graph? Where are the intersections between the two? What do these intersections represent? (3) Find the points where the hours of daylight are at a maximum/minimum. Around what time of the year are these points? Compare the information. (4) What tools did you use to solve this problem? What other ways could you have come to find the same solution? (5) How many hours of daylight are in each location at t=5? at t=8?

I used part of the UbD template to present my Performance Task 1. It is attached in the word document educ519precalc. Essential questions, relative standards, goals and understandings are all included in this format. The details of the performance task are also included.

I've included the rubric I will hand to my students that show the requirements for a total of 15 possible points.

After students complete the performance task they will be paired up in a Think, Pair, Share with the original assignment handout to make sure they included all the teacher required.


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