Trigonometry

Grade Level (can be multiple): 11-12

Brief Overview of Course:
This one semester course is designed for students to understand practical applications of trigonometry. It also emphasizes estimation and logic. The following topics are covered:
-Definitions of Sine, Cosine and Tangent
-Inverse functions
-sine law and proof
-cosine law and proof
-area of a triangle and proof
-Cartesian to polar coordinate conversion
-practical world problems
-Trig equations including factoring
-solving triangles given a minimum of information
-drawing diagrams to scale
-angle measure conversion from radians to degrees
-graphing trig functions
-solving logic puzzles

Readings: 
Math Puzzles and Games by Michael Holt
Algebra and Trigonometry by James stewart, Lothar Redlin and Salem Watson
Precalculus Mathematics in a Nutshell By George F. Simmonms
Media Used: 
Calculators
Interim Assessments: 

Students work outdoors, using a building they can walk around completely. The Flat Iron Building at 23rd Street and 5th Avenue is a good example. Students are asked to determine the volume of the building to the nearest cubic meter. They then determine which formula to use and must show all calculations, the tools used, and how they used them. They then explain if their answer makes sense, using logic and examples (other than trig) to show how they could estimate the answer. Finally, they make a scale drawing labeling everything.

Significant Assignments: 

To make trigonometry relevant, other locations in the city are used. For example, students may determine the height of the smoke stakes on Roosevelt Island from our location in Manhattan at 63 Street and the East River. They then complete the following 4 pages:
page 1) Explain in detail exactly what your procedure was. What tools did you use and how did you use them?
page 2) Show all of your formulas and calculations. Does your answer make sense? Why or why not? Explain using logic and examples (other than trig) of how you could estimate the answer. State this estimation.
page 3) Sketch to scale, as best you can, the picture of this problem. Be sure to label everything and state the scale. Label your sheet of graph paper.
page 4)
A) What difficulties did you have at any point in your procedure? How could you have avoided them?
B) What other way could you have solved this problem? Be specific in your explanation.

Significant Activities or Projects: 

We take the Staten Island Ferry from Manhattan to Staten Island and return. Before we leave, students research the height of the Statue of Liberty from the water's edge. From this information and data they collect from both docks by using simple tools, they determine the distance from Manhattan to Staten Island.
They then complete a 4-page paper:
page 1) Explain in detail exactly what your procedure was. What tools did you use and how did you use them?
page 2) Show all of your formulas and calculations. Does your answer make sense? Why or why not? Explain using logic and examples (other than trig) of how you could estimate the answer. State this estimation.
page 3) Sketch to scale, as best you can, the picture of this problem. Be sure to label everything and state the scale. Label your sheet of graph paper.
page 4)
A) What difficulties did you have at any point in your procedure? How could you have avoided them?
B) What other way could you have "done" this problem? Be specific in your explanation.

Sample PBATs: 
Students apply the skills they have acquired through the semester, using trig to calculate distances between two well-known NYC sites. For example, a student may be asked to find the distance from the Empire State building to the Williamsburg Bank building, using a vantage point on Governor's Island in New York Bay and based on their knowledge of the heights of both buildings. Students are told: You have with you: Trig tables, 100 feet of tape, balloons, a scientific calculator, an axe, binoculars, a hammer, a ball of twine, graph paper and colored pencils, a Polaroid camera, a sextant (angle measurer), a thermos of tea (two liters), a yard stick, peanut butter sandwiches, tent pegs, and a mirror You may not go in the water, nor may you throw anything in the water. Your method must be efficient (minimize time and energy) and must involve as much trig as possible to solve the distance problem. Draw diagrams and label everything. Show which equations you will use and how you will use them. When you have done this estimate the distance without using trig. What difficulties did you have at any point in your procedure? How could you have avoided them? What other way could you have "done" this problem? Be specific in your explanation.