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 1493 views around the world You can reuse this answer Creative Commons License