the tangent line to the graph of y=sin x at the point (2pi/3, (radical 3)/2) crosses the sine graph at the point where x=?
2 answers
5.388
Steps:
y=sinx
y'=cosx
slope of tangent: cos(2pi/3)=-1/2
equation of tangent: y-(sqrt3/2)=-1/2(x-2pi/3) > y=-1/2x+1.9132
find when tangent line = f(x) to see where the graph crosses
sinx=-1/2x+1.9132 > put into desmos
x=5.388
y=sinx
y'=cosx
slope of tangent: cos(2pi/3)=-1/2
equation of tangent: y-(sqrt3/2)=-1/2(x-2pi/3) > y=-1/2x+1.9132
find when tangent line = f(x) to see where the graph crosses
sinx=-1/2x+1.9132 > put into desmos
x=5.388