What is the slope of the tangent line of #r=(2theta+sin2theta)/cos^2theta# at #theta=(-3pi)/8#? Calculus Polar Curves Determining the Slope and Tangent Lines for a Polar Curve 1 Answer Monzur R. Apr 16, 2017 #"m"_"tan"=16+8sqrt2+(12+9sqrt2)pi# Explanation: #(dr)/(d theta)=((cos^2theta)(2+2cos2theta)+(2costhetasintheta)(2theta+sin2theta))/cos^4(theta)# #r'(-3/8pi)=# #((cos^2(-3/8pi))(2+2cos2(-3/8pi))+(2cos(-3/8pi)sin(-3/8pi))(2(-3/8pi)+sin2(-3/8pi)))/cos^4((-3/8pi))# #=16+8sqrt2+(12+9sqrt2)pi# 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 1364 views around the world You can reuse this answer Creative Commons License