MTH1014 Quiz 10

Fall 2013
Herbert J. Bernstein ( )

MTH1014 Quiz 10
Fall 2013


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This is quiz 10 to be taken by Tuesday, 3 December 2013. It should take you between half an hour and 2 hours to answer the following questions. You should do this quiz after doing the rest of assignment 10'.

  <==== Do this AFTER you've answered all the questions

You probably DON'T want to do this ===>  

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Please answer the following questions on this form (or on a paper copy of this form).

  1. Carefully define polar coordinates and explain how to covert between polar coordinates and rectangular coordinates (also known as rectangular coordinates.

  2. Convert the following rectanguar coordinates to polar coordinates: (0,0), (1,0), (.7071067811865476,.7071067811865476), (0,1),(-.7071067811865476,.7071067811865476), (-1,0), (-.7071067811865476,-.7071067811865476), (0,-1), (.7071067811865476,-.7071067811865476)

  3. Convert the following polar coodinates to rectangular coordinates, assuming angles are given in radians: (0,0), (1,0), (0,1), (1,1), (-1,0), (-1,-1)

  4. Carefully explain the tests for symmetry in polar equations.

  5. Carefully explain the equations for cardiods, limacons (with ans without inner loop), roses and lemniscates with words and formulae, not pictures.

  6. Carefully explain the polar form of a complex number, and explain the terms magnitude and argument in the context of the polar form of a complex number

  7. Carefully state and explain De Moivre's Theorem and use it to find all the complex fifth roots of -32. You may leave your answers in polar form with the argument in degreees

  8. Carefully explain in words (not with pictures) how to add or subtract two algebraic vectors and how to multiply an algebraic vector by a scalar

  9. Carefully explain in words (not with pictures) how to find a vector from its direction and magnitude.

  10. For each of the following pairs of vectors, compute the dot product, the angle between the vectors and state whether the vectors are orthogonal or parallel: (0,0) and (1,1); (1,-1) and (1,1); (2,2) and (3,3); (2,-2) and (1,5)

  <==== Do this AFTER you''ve answered all the questions

You probably DON'T want to do this ===>  

Revised 22 April 2013