When someone learns about the unit circle, he/she often uses a reference circle to learn where the different values of Pi are located on the unit circle. A reference circle is a circle with multiple of Pi, Pi/2, Pi/3, Pi/4, and Pi/6 marked. Each angle has a line from the origin to the point of the angle.

Using your knowledge of the plots package, the plottools package, display(), line(), circle(), and textplot(), create a reference circle with all angles marked. Use a different line color for each set of multiples (i.e. black for x*Pi; red for x*Pi/2; etc.) You may not use any commands that we haven't mentioned.

Solution:

> restart:with(plottools):with(plots):

> g:=circle([0,0],1,thickness=3):

> a:=line([cos(5*Pi/4), sin(5*Pi/4)], [cos(Pi/4), sin(Pi/4)], x=-1..1, -1..1, color=red, thickness=3):

> b:=line([cos(7*Pi/6), sin(7*Pi/6)], [cos(Pi/6), sin(Pi/6)], x=-1..1,-1..1,color=blue, thickness=3):

> c:=line([cos(4*Pi/3), sin(4*Pi/3)], [cos(Pi/3), sin(Pi/3)], x=-1..1, -1..1, color=green, thickness=3):

> d:=line([cos(3*Pi/4), sin(3*Pi/4)], [cos(7*Pi/4), sin(7*Pi/4)], x=-1..1, -1..1, color=red, thickness=3):

> e:=line([cos(5*Pi/6), sin(5*Pi/6)], [cos(11*Pi/6), sin(11*Pi/6)], x=-1..1,-1..1,color=blue, thickness=3):

> f:=line([cos(2*Pi/3), sin(2*Pi/3)], [cos(5*Pi/3), sin(5*Pi/3)], x=-1..1, -1..1, color=green, thickness=3):

> t1:=textplot([cos(Pi/6)+.1,sin(Pi/6)+.1,"Pi/6"]):

> t2:=textplot([cos(Pi/4)+.1,sin(Pi/4)+.1,"Pi/4"]):

> t3:=textplot([cos(Pi/3)+.1,sin(Pi/3)+.1,"Pi/3"]):

> t4:=textplot([cos(5*Pi/6)-.1,sin(5*Pi/6)+.1,"5Pi/6"]):

> t5:=textplot([cos(3*Pi/4)-.1,sin(3*Pi/4)+.1,"3Pi/4"]):

> t6:=textplot([cos(2*Pi/3)-.1,sin(2*Pi/3)+.1,"2Pi/3"]):

> t7:=textplot([cos(7*Pi/6)-.1,sin(7*Pi/6)-.1,"7Pi/6"]):

> t8:=textplot([cos(5*Pi/4)-.1,sin(5*Pi/4)-.1,"5Pi/4"]):

> t9:=textplot([cos(4*Pi/3)-.1,sin(4*Pi/3)-.1,"4Pi/3"]):

> t10:=textplot([cos(11*Pi/6)+.1,sin(11*Pi/6)-.1,"11Pi/6"]):

> t11:=textplot([cos(7*Pi/4)+.1,sin(7*Pi/4)-.1,"7Pi/4"]):

> t12:=textplot([cos(5*Pi/3)+.1,sin(5*Pi/3)-.1,"5Pi/3"]):

> t13:=textplot([cos(Pi/2),sin(Pi/2)+.1,"Pi/2"]):

> t14:=textplot([cos(Pi)-.1,sin(Pi),"Pi"]):

> t15:=textplot([cos(3*Pi/2),sin(3*Pi/2)-.1,"3Pi/2"]):

> t16:=textplot([cos(2*Pi)+.1,sin(2*Pi),"2Pi"]):

> l1:=line([-1,0],[1,0],thickness=2,color=black):

> l2:=line([0,-1],[0,1],thickness=2,color=black):

> display(g, a, b, c, d, e, f, t1, t2, t3, t4, t5, t6, t7, t8, t9, t10, t11, t12, t13, t14, t15, t16, l1, l2, scaling=constrained, axes=none);

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