Polar Geometry & Trigonometry

Trivium

  1. Given an origin point and a coordinate axis in the plane, use a protractor and ruler to determine the polar coordinates of any point in that plane.
  2. Given either the rectangular or polar coordinates of a point in space write down its coordinates in the other system.
  3. Given an angle expressed in radian, or in degrees/minutes/seconds, or as a fraction of a degree, express it the other two ways.
  4. Given an analytic description (equation) of a curve in either rectangular or polar coordinates, write down a description in the other coordinate system.
  5. Know the output value of any trigonometric function at any rational multiple of \(\frac{\pi}{6}\) (30°) or \(\frac{\pi}{4}\) (45°).
  6. Given composite of a trigonometric function with any number of linear functions sketch its graph, and conversely recognize the graph of such a function and write down its formula.

Problems

  1. What is the distance between the points \((3,45°)?\) and \((5,210°)?\)

    In general, given two points \((r_1, \theta_1)\) and \((r_2, \theta_2),\) what is a formula for the distance between them?

  2. What is the degree measure of an angle that measures one radian? How do you express this degree measure in degrees/minutes/seconds?
  3. TK Angle of elevation and depression.
  4. TK Bearing