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SOMETHINGS' MATHEMATICAL,     TOO


  CHORDS AND SINES

Lesson title :                 Chords and Sines

Subject and Grade Level :    10 - 12th grade Mathematics

Brief Description :     To discover the mathematical relationships between chords of a circle and the sine of an angle in a right triangle.

Objectives —The students will be able to:

    1.    Explore required definitions through web based diagrams.

    2.    Discover the mathematical relationships between a chord and the sine of an angle cutting a portion of a circle.

    3.    Communicate mathematical concepts in writing.

Educational/Skills Goals (Include academic (standards) and Internet goals)

    1.  Reflect upon and clarify their thinking about mathematical ideas and relationships.

    2. Express mathematical ideas orally and in writing.

    3.  Read written presentations of mathematics with understanding.

Materials:

    Computer with Internet accessJava enabled browserWord Processor program

Internet resources involved (web addresses)

Procedure:

  • Go to the site for Definitions and read the first two paragraphs and note the new definition of the sine function.
  • Examine the first Java Applet - a diagram depicting this new definition.
  • Experiment with changing segment lengths and angle measures by clicking and dragging on any point on the diagram.  Look carefully at the right triangles as you drag points. Make notes of your observations.
  • Continue reading  the Definitions page and try to vizualize what the author is proving.  Make notes if necessary.  Record the major steps in the author's proof.
  • Write an explanation of this informal proof  of the sine function  by describing the relationship between the standard definition  and the new definition.   Include both the definitions in your writing in addition to the concepts of right angles  and similarity.  Include diagrams where appropriate.

Timeline:  1 - 3 days depending on availability of computers,  Internet access and ability levels of students.

Non-Internet Activities:  Class work reiterating trigonometric ratios,  relationships in right triangles and properties of chords in a  circle.

Internet Activities:  See above under procedure.

Assessment (Evaluation):

Holistic Scale

  • 3         Response is exemplary, detailed and clear.
  • 2         Response is generally correct.
  • 1         Response is partially correct, but lacks clarity.
  • 0         No response or response is incorrect.

Follow-up Activities and Extensions:  Go to the site for Trigonometry for a complete view of trigonometry from angle measure to identities.  Use the calculator site as and when required. Minimize the window and keep it available on your desktop.

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After the lesson is taught, review the following:

    Set-Up Time Required

    Class Time Required

    Problems and Issues that were encountered

    Successes

    Recommendations for Improvement

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