Math 142

Summer 2000

Final Exam

 

  1. (15 pt) Use the following triangle to find all trigonometric functions of the angle q.

 

 


                                               y                               q

 

                                                                x

 

  1. (18 pt) Two cannonballs are fired, both with initial velocity  The first is fired at an angle of  where  The second is fired at an angle of

a)      Find the parametric equations for the motion of the first cannonball.

b)      Find the parametric equations for the motion of the second cannonball.

c)      Which cannonball goes farther?

 

  1. (12 pt) What is the period, amplitude and phase shift of the function  Use this information to sketch the curve.

 

  1. (15 pt) Graph the polar equation  (Hint: the previous problem should prove useful. Also use two complete periods to help you out.)

 

  1. (18 pt) Consider the vectors  and

a)      Let  and compute

b)      Also with  compute

c)      Find all values of  so that the vectors are orthogonal.

 

  1. (20 pt) Solve the following triangle:

 


                                                                      x

                     

                                                                                                        3Ö3                   

 


                                                                                             150°

                                                              2

 

  1. (12 pt) Solve the following trigonometric equations:

a)

b)