a.  Express the angle theta as a function of h. 

     = .


b.  Express the length of the arc, s, as a function of theta. (Don’t forget about radian measure) 

    s = .


c.  Use composition of functions to find the length of the arc, s, as a function of h. 

    s = .


d.  Since the angle and the arc length are both functions of the height of the satellite, it is this height that determines their values. 

    Build a table for both functions showing their values for heights ranging from 0 miles to 1000 miles in increments of 100 miles. 

    h, in miles	    theta (radians)	s, in miles
		
     100	     0.222	           1761
     200	     0.311	           2466
     300	     0.378	           2990
     400	     0.432	           3419
     500	     0.478	           3786
     600	     0.519	           4109
     700	     0.555	           4397
     800	     0.588	           4659
     900	     0.618	           4898
    1000	     0.646	           5118


e.  Try using some values of h greater than 1000 to see what happens to theta and s, then discuss, intuitively, (using common sense), 

    what the angle, theta, and the arc length, s, approach as h increases to infinity. Now, relate these ideas to the terms “domain” and “range”.