Math 142

Summer 2000

Exam 1

 

  1. (12 pt) Change the following from degrees to radians or vice versa, then list an angle in standard position that is between 0 and 2p (if you are in radians) or 0 and 360° (if you are in degrees) that is coterminal with your angle:

a) -972°           b) 39p/8

 

2.      (4 pt) Suppose that you have an angle, q, such that tan(q)<0 and sec(q)>0. In which quadrant does the terminal side of the angle lie?

  1. (14 pt) Suppose that  and that  is positive. Find values for all the trigonometric functions of the angle

 

  1. (20 pt) Consider the following triangle:

 

 

 

 

                            a

 

                                                            q

                                                      

                                                  2a

      Find all trigonometric functions of the angle q.

 

  1. (20 pt) Find the precise values of the following without using a calculator.

a) b)  

c)

d)

 

  1. (20 pt) A lighthouse has a single light that rotates every three seconds. If you are standing at a distance of 2 miles from the lighthouse, how fast do you perceive the beam of light to be traveling in miles per hour?

 

  1. (20 pt) Robin Hood aims his arrow right at the bull’s-eye of an archery target that has a diameter of 8 feet. Right as he shoots, he catches the eye of Maid Marian and the distraction changes his shot by 2°. The arrow hits the target right on the edge. How far is Robin Hood from the target?