What is the slope of #r=tantheta-theta# at #theta=pi/8#? Calculus Polar Curves Determining the Slope and Tangent Lines for a Polar Curve 1 Answer AltairSafir Mar 19, 2018 Derivative with Polar Coordinates is # (\partial x) / (\partial y) = ((\partial r) / (\partial theta) sin(theta)+ rcos(theta))/((\partial r) / (\partial theta) cos(theta)- rsin(theta)# Explanation: #(\partial r) / (\partial theta) = 1/cos^2(theta)+1# #r(theta = pi/8)=0.0 22# # (\partial x) / (\partial y) = (tan(theta)/cos(theta)+sin(theta)+rcos(theta))/(1/cos(theta)+cos(theta)-rsin(theta))# # (\partial x) / (\partial y)(theta=pi/8) =1.57 # Answer link Related questions How do you find the slope of the tangent line to a polar curve? How do you find the slope of a polar curve? How do you find the equation of the tangent line to the polar curve #r=3+8sin(theta)# at #theta=pi/6# ? How do you find the slope of the polar curve #r=3+8sin(theta)# at #theta=pi/6# ? How do you find the slope of the polar curve #r=cos(2theta)# at #theta=pi/2# ? How do you find the slope of the polar curve #r=1+sin(theta)# at #theta=pi/4# ? How do you find the slope of the polar curve #r=3sec(2theta)# at #theta=pi/6# ? How do you find the equation of the tangent lines to the polar curve #r=sin(2theta)# at #theta=2pi# ? How do you find the equation of the tangent lines to the polar curve #r=4cos(theta)# at #theta=0# ? What is the slope of #x-2y=2#? See all questions in Determining the Slope and Tangent Lines for a Polar Curve Impact of this question 1958 views around the world You can reuse this answer Creative Commons License