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# Radian Measure and the Unit Circle

11
Subject:
Trigonometry
Goal Summary:
Understanding and Converting from degree measure to radian measure for the purpose of solving real problems in Trigonometry that involve Arc Length, Angular Velocity and Linear Velocity.
Standards Met:
IDs Only
Detail
Essential Questions:
Why do we have to learn radians, when we already have perfectly good degrees? (Because degrees, technically speaking, are not actually numbers, and we can only do math with numbers. This is somewhat similar to the difference between decimals and percentages. Yes, "83%" has a clear meaning, but to do mathematical computations, you first must convert to the equivalent decimal form, 0.83)
Understandings:
Students should understand how to find each of the six trigonometric circular functions values with the use of a unit circle. To find the length of an arc intercepted by a central angle and to determine the speed at which a point on the circle moves in terms of its distance and its angle.
Content Goals:
Radian Measure, Application of Radian Measure, The Unit Circle and Circular Functions, Linear and Angular Velocity.
Skill Goals:
The students will be able to define radian measure and use it to find arc length, area of a sector, angular velocity and linear velocity. The students will be able to find exact values of the six trigonometric functions defined by the unit circle.
Other Information:
Key Terms learned: radian, circumference, latitude, sector of a circle, longitude, subtend, unit circle, circular functions, reference arc, linear speed, angular speed.
Reflection:
As much as I emphasized students to memorize the exact values for each of the trigonometric functions for the special angles it seems even more important as we begin this section. Students struggling to recall their values makes the discussion of the idea of the unit circle less effective. More emphasis on Choosing a level of accuracy appropriate to limitations on measurement when reporting quantities is needed. Have students use units as a way to understand problems and to guide the solution of multi-step problems.