Fix bug 4689

Author: gajennings

OpenProblemLibrary/Wiley/setAnton_Section_3.1/Anton3_1_Q18.pg

@@ -43,18 +43,22 @@ $a=non_zero_random(-8,8,1);
 # If the answer is tested at random values of x and y 
 # a student might substitute cos(y)->x/a in the 
 # implicit solution and have it marked "incorrect" 
-# so we'll numerically generate a series of test points along the 
-# implicit curve and test it on those points.  
+# so we'll generate 8 test points along the 
+# implicit curve x=a*y*sec(y) and test it on those points.  
 
 $ans=Formula("-cos(y)*([2*$a*sin(y)+x*(1+sin(y)^2)]/($a+x*sin(y))^3)")->reduce;
 
-$ans->{test_points} = [ [0,0],
-  [$a*0.2, 0.19616428118783816 ],[-$a*0.2, -0.19616428118783816 ], 
-  [$a*0.4, 0.37255949583211007], [-$a*0.4, -0.37255949583211007],
-  [$a*0.6, 0.5205326392380185],  [-$a*0.6, -0.5205326392380185], 
-  [$a*0.8, 0.641134282813549],   [-$a*0.8, -0.641134282813549],
-  [$a,     0.7390851332151331 ], [-$a,     -0.7390851332151331 ]
-];
+# 8 test points between y=-pi/3 and y=pi/3
+
+@test_pts = ();
+$inc = pi/12;
+for ($i=0; $i<9; $i++){
+  $y = -pi/3+$i*$inc;
+  $x = $a*$y*sec($y);
+  push(@test_pts,[$x,$y]);
+}
+
+$ans->{test_points} = @test_pts; 
 
 ###################################
 # Main text