1. Topic-
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| The Unit Circle and Trigonometric Ratios |
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2. Content-
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| The six trigonometric ratios and their relationship to the x- and
y-coordinates of the points lying on the Unit circle having radius
one unit in length |
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3. Goals: Aims/Outcomes-
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1. Relate the unit circle to conic sections and the equation of
a circle template
2. Discover how the rules of right triangle trigonometry relate to
points on the unit circle
3. Be able to give the values of trigonometric ratios of any angle
using the unit circle |
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4. Objectives-
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1. To teach students to apply prior knowledge to familiar, but new
material to unlock new mathematical concepts in trigonometry
2. To encourage students to realize that mathematics is discovered,
rather than created, using current knowledge applied with imagination |
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5. Materials and Aids-
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-TV and DVD player
-DVD of "Flatland", the movie
-compass
-graph paper
-protractor |
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6. Procedures/Methods-
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A. Introduction-
1. Watch the movie "Flatland" and connect its concepts of 0, 1,
2, and 3 dimensions to their graphical/geometrical representations
2. Take a simple 5 question quiz (enclosed) to survey and focus their
attention to geometrical applications of Algebra |
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B. Development-
1. Go over the answer to the Flatland quiz together and discuss
the dimensions we know in our world today
2. Draw a picture of a circle centered at the origin with a radius
of 1 unit and have the students come up with its equation
3. Explain the basics of the unit circle and how the Pythagorean theorem
is used to derive the circle equation using the coordinates of points
on lying on the circle
4. Recall/re-explain the geometric ratios of the lengths of the sides
of a 30-60-90 degree right triangle and a 45-45-90 degree right triangle |
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C. Practice-
1. Have the students create the unit circle on graph paper using
a compass and label the parts of the circle
2. Have the students create a 30-60-90 degree right triangle and use
the relationship of the sides to build the trigonometric rations of
the angle created at the origin by the x-axis and the terminal side
3. Have the students do the same as #2. for a 45-45-90 right triangle
inscribed in the unit circle
4. Lead the students to apply transformations of those angles around
the origin to create one period around the unit circle |
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D. Independent Practice-
| Apply the usefulness of the unit circle to answer homework/practice
questions over the trigonometric ratios of familiar angles (enclosed) |
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E. Accommodations (Differentiated Instruction)-
| Provide more time the next day in class if needed for students to
allow them to be able to discover the unit circle mathematics in a
less stressful environment |
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F. Checking for understanding-
| Ask students for questions and re-explain any topics that are unclear |
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G. Closure-
Relate the angles in degrees to their equivalent radian measure
and explain the trigonometric ratios are the same value no matter
the units of the angle measures being used
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7. Evaluation-
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1. Collect the homework practice the next day and grade it to assess
understanding
2. Give a quiz the next day in class after answering questions over
the homework and grade for assessment purposes |
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