What is the equation of the line that is normal to #f(x)=cscx+tanx-cotx # at # x=-pi/3#? Calculus Derivatives Normal Line to a Tangent 1 Answer 1s2s2p Feb 23, 2018 #y=-(3x)/14-2.53# Explanation: #"Tangent":d/dx[f(x)]=f'(x)# #"Normal":-1/(f'(x))=-1/(d/dx[cscx+tanx-cotx])=-1/(d/dx[cscx]+d/dx[tanx]-d/dx[cotx])=-1/(-cscxcotx+sec^2x+csc^2x)# #-1/(f'(-pi/3))=-1/(-csc(-pi/3)cot(-pi/3)+sec^2(-pi/3)+csc^2(-pi/3))=-1/(14/3)=-3/14# #y=mx+c# #f(a)=ma+c# #csc(-pi/3)+tan(-pi/3)-cot(-pi/3)=-pi/3(-3/14)+c# #c=csc(-pi/3)+tan(-pi/3)-cot(-pi/3)+pi/3(-3/14)# #c=-2.53# #y=-(3x)/14-2.53# Answer link Related questions What is a Normal Line to a Tangent? What is a Normal Line to a curve? How you would find the equation of a line normal to a curve? How do you find the equation of a normal line to a curve at a given point? How do you give the equation of the normal line to the graph of #y=2xsqrt(x^2+8)+2# at point (0,2)? What are some applications in which you need to find the normal to the tangent line? How do you find the equation of the tangent line and normal line to the curve #y = (5+6x)^2# at... What is the normal line to the tangent line at a point on a curve? What is the equation of the normal line of #f(x)=x^3 + 3x^2 + 7x - 1 # at #x=-1 #? What is the equation of the normal line of #f(x)=x^3/(3x^2 + 7x - 1 # at #x=-1 #? See all questions in Normal Line to a Tangent Impact of this question 1158 views around the world You can reuse this answer Creative Commons License