Extra Credit Problems
Fourth Six Weeks

Instructions:
  1.  Problems may be submitted any time during the six weeks, but they MUST be turned by the due date.
        (Due Date:  Feb 12, 2008)
  2.  Your work must accompany each problem.  No credit will be given for just an answer.
  3.  Parts of problems are worth anywhere from 1 - 3 points depending on level of difficulty.
       Credit is given only for correct work and answers. The whole part must be correct to
       receive credit.
  4.  You may do as many or as few problems as you desire. Try to keep them in order.

Problems:
  1. Use DeMoivre's Theorem to derive an identity for sin 3q  in terms of cos q and sin q.

    2.  
  2. A fuel tank has a cross section whose shape is a 2 m by 2 m square capped at the top and bottom

    3. by semicircles.  Use a computer or graphing calculator to determine how to mark a measuring rod
    to show that the tank is only 10% full.
     
  3. A goat is tethered to a stake at the edge of a circular field with radius 1 unit.  Use a computer

    4. or graphing calculator to determine how long the rope should be so that the goat can graze over
    half the field.
     
  4. From the southeast corner of the cemetery on Burnham Road, proceed S 78o W for

    5. 250 m along the southern boundary of the cemetery until a granite post is reached, then
    S 15o E for 180 m to Allard Road, then N 78o E along Allard Road until it intersects
    Burnham Road, and finally N 30o E along Burnham Road back to the starting point.
    Find the area of this plot of land.
     
  5. Evaluate sin [Tan-1(1/2) + Tan-1(1/3)] without using a calculator or tables.

    6.  
  6. Verify that 4 Tan-1(1/5) - Tan-1(1/239) = p/4

    7. (Hint:  Let a = Tan-1(1/5) and let b = Tan-1(1/239).  Then find tan (4a - b).)
     
  7. Solve for x for 0 <  x < 2p:

    8. a.  sin 3x = sin 5x + sin x
    b.  Tan-12x = Sin-1x
     
  8. Find the coordinates of the point 4/5 of the way from A(7,-2) to B(2,8).

    9.  
  9. Let x and y be positive integers such that x + y < 13 and 3x + y < 24.  Find the maximum value of 4x + y:

    10.  
  10. Graph |x| + |y| = 2 without a calculator.

    11.  
  11. Graph |2x - 3y| < 6 without a calculator.


    12. (All of the above problems were taken from Advanced Mathematics by Richard G. Brown, Houghton Mifflin, 1992)