LAC07 More Trig MrG 2013.0529

3111 days ago by LAC2013

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


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


#8) Double Angle show(cos(2*x)) show(cos(2*x).simplify_trig()) show(plot(cos(x)^2)) show(plot((1+cos(2*x))/2)) 
       




#9) Double Angle show(sin(2*x)) show(sin(2*x).simplify_trig()) show(plot(sin(x)^2)) show(plot((1-cos(2*x))/2)) 
       




#10) Euler's Identity show(taylor(e^x,x,0,8)) show(taylor(e^(i*x),x,0,8)) show(taylor(cos(x),x,0,8)) show(i*taylor(sin(x),x,0,8)) show(bool(e^(i*x)==cos(x)+i*sin(x))) 
       




#11) loose ends! show(expand((x+1)^2)) show(factor(x^2+2*x+1)) show(diff(x^2+2*x+1,x)) show(diff((x+1)^2,x)) show(integrate(x^2+2*x+1,x,0,1))