1. The square root of 30.

  2. Approximately 0.315425 radians.

  3. Let 

    
a = (1, 3, 2, 4)
b = (3, 1, -2, 4)
c = (4, 4, -1, -1)

    The lengths of the three sides are 

    
||b - a|| = the square root of 24
||c - b|| = 6
||c - a|| = the square root of 44

    The angle at the vertex 

    
a is approximately 1.05599 radians
b is approximately 1.29515 radians
c is approximately 0.79045 radians

  4. Yes.

  5. Yes.

  6. Approximately 0.774037 t.

  7. 0.

  8. (1/2) sin t

  9. (1/2) sin t

  10. Approximately 0.866025 cos t

Copyright c 1995 by Frank Wattenberg, Department of Mathematics, Montana State University, Bozeman, MT 59717