LAC06 Trig MrG 2013.0528

3114 days ago by LAC2013

#1) Pythagorean f(x)=sin(x)^2+cos(x)^2 show(f(x)) show(f(x).simplify_trig()) show(bool(f(x)==1)) plot(f(x),xmin=-1,xmax=1,ymin=0,ymax=2) 
       



#2) Pythyagorean g(x)=f(x)/cos(x)^2 show(g(x)) show(g(x).simplify_trig()) show(bool(g(x)==sec(x)^2)) show(plot(g(x))) show(plot(sec(x)^2)) 
       





#3) Pythyagorean h(x)=f(x)/sin(x)^2 show(h(x)) show(h(x).simplify_trig()) show(bool(h(x)==csc(x)^2)) show(plot(h(x),xmin=.1,xmax=2)) show(plot(csc(x)^2,xmin=.1,xmax=2)) 
       





#4) Sum of 2 Angles var('y') show(cos(x+y)) show(cos(x+y).simplify_trig()) show(plot3d(cos(x+y),(x,-2,2),(y,-2,2)),viewer='tachyon') show(plot3d(cos(x)*cos(y)-sin(x)*sin(y),(x,-2,2),(y,-2,2)),viewer='tachyon') 
       


#5) Sum of 2 Angles var('y') show(cos(x-y)) show(cos(x-y).simplify_trig()) show(plot3d(cos(x-y),(x,-2,2),(y,-2,2)),viewer='tachyon') show(plot3d(cos(x)*cos(y)+sin(x)*sin(y),(x,-2,2),(y,-2,2)),viewer='tachyon')