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Mathematics, Tmm0022
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The Unit Circle and Cosine and Sine Functions


TMM 002 PRECALCULUS (Revised March 21, 2017)

2.  Geometry  

     2b.  Analyze right triangles.  Routine analysis of side lengths and angle measurements using trigonometric ratios/functions as well as the Pythagorean Theorem.*

Sample Tasks:

  • The student can solve right triangles numerically using trigonometric ratios and relationships.
  • The student can compare similar triangles numerically.
  • The student can describe relationships within or between right/similar triangles algebraically using trigonometric ratios and relationships.

The Unit Circle and the Cosine and Sine Functions


    In this module we will introduce and study the two basic trigonometric functions – Cosine and Sine. As we will see any point in the x-y plane is some (radial) distance r away from the origin on a line through the origin. Since a line through the origin is inclined at some angle θ the coordinates  of x and y  of any point in the plane can be written in terms r  and cosine and sine of the angle θ.

    Review: Pythagorean Theorem for right angle triangles, positive and negative angles, radian and degree measures.

    Learning Objectives:

    • Equation of a circle of radius r and center (0,0e).
    • Equation of the Unit Circle
    • Reference angle
    • Definition of Cosine and Sine
    • Domain and Range of the Cosine and Sine Functions