Determining the Slope and Tangent Lines for a Polar Curve

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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#?
• What is the equation of the tangent line of #r=sintheta + costheta# at #theta=pi/2#?
• What is the equation of the tangent line of #r=tan^2theta - costheta# at #theta=pi/4#?
• What is the equation of the tangent line of #r=cot^2theta - sintheta# at #theta=pi/4#?
• What is the equation of the tangent line of #r=tan^2theta - sintheta# at #theta=pi/4#?
• What is the equation of the tangent line of #r=tan^2(theta) - sin(theta-pi)# at #theta=pi/4#?
• What is the equation of the tangent line of #r=2cos(theta-pi/2) + sin(2theta-pi)# at #theta=pi/4#?
• What is the equation of the tangent line of #r=2cos(theta-pi/2) - sin(2theta-pi)# at #theta=pi/4#?
• What is the equation of the tangent line of #r=cos(theta-pi/2)/sintheta - sin(2theta-pi)# at #theta=(-3pi)/8#?
• What is the equation of the tangent line of #r=cos(2theta-pi/4)/sintheta - sin(theta-pi/8)# at #theta=(-3pi)/8#?
• What is the equation of the tangent line of #r=cos(theta+pi/2)*cos(theta-pi) # at #theta=(-pi)/8#?
• What is the equation of the tangent line of #r=cos(theta-pi/4) +sin^2(theta+pi)-theta# at #theta=(-13pi)/4#?
• What is the equation of the tangent line of #r=cos^2(theta-pi) +sin^2(theta-3pi)-theta# at #theta=(-13pi)/4#?
• What is the equation of the tangent line of #r=4cos(-theta+(5pi)/6) +sin(theta)# at #theta=(7pi)/12#?
• What is the equation of the tangent line of #r=4cos(-theta+(3pi)/2) +sin(-theta)# at #theta=(-5pi)/12#?
• What is the equation of the tangent line of #r=2cos(theta-(3pi)/4) +2sin(-theta+(3pi)/2)# at #theta=(-5pi)/12#?
• What is the equation of the tangent line of #r=-5cos(-theta-(pi)/4) + 2sin(theta-(pi)/12)# at #theta=(-5pi)/12#?
• What is the equation of the tangent line of #r=cos(theta+(5pi)/4) * sin(theta-(17pi)/12)# at #theta=(-5pi)/12#?
• What is the equation of the tangent line of #r=cos(-3theta-(2pi)/3) # at #theta=(-5pi)/3#?
• What is the equation of the tangent line of #r=6cos(theta-(2pi)/3) # at #theta=(-5pi)/3#?
• What is the equation of the tangent line of #r=-2sin(6theta-(4pi)/3) # at #theta=(2pi)/3#?
• What is the equation of the tangent line of #r=theta-sin(-theta+(pi)/3) # at #theta=(2pi)/3#?
• What is the equation of the tangent line of #r=theta-3sin(theta+(5pi)/3) # at #theta=(2pi)/3#?
• What is the equation of the tangent line of #r=5theta + 2sin(4theta+(2pi)/3) # at #theta=(2pi)/3#?
• What is the slope of #r=sintheta# at #theta=pi#?
• What is the slope of #r=tantheta-theta# at #theta=pi/8#?
• What is the slope of #r=tantheta^2-theta# at #theta=(3pi)/8#?
• What is the slope of #r=tantheta^2-theta^2-theta# at #theta=(3pi)/8#?
• What is the slope of #r=thetacostheta/2-theta^2sintheta# at #theta=(3pi)/8#?
• What is the slope of the tangent line of #r=3sin(theta/2-pi/4)# at #theta=(3pi)/8#?
• What is the slope of the tangent line of #r=theta-sin((10theta)/3-(pi)/8)# at #theta=(pi)/4#?
• What is the slope of the tangent line of #r=theta-sin((theta)/3-(2pi)/3)# at #theta=(pi)/4#?
• What is the slope of the tangent line of #r=theta-sin((theta)/6+(2pi)/3)# at #theta=(pi)/4#?
• What is the slope of the tangent line of #r=theta-sin((theta)/6+(2pi)/3)# at #theta=(pi)/6#?
• What is the slope of the tangent line of #r=2theta-3sin((13theta)/8-(5pi)/3)# at #theta=(7pi)/6#?
• What is the slope of the tangent line of #r=theta/3+sin((3theta)/8-(5pi)/3)# at #theta=(7pi)/6#?
• What is the slope of the tangent line of #r=theta/3+sin((3theta)/8+(5pi)/3)# at #theta=(11pi)/8#?
• What is the slope of the tangent line of #r=2theta+3cos((theta)/2-(2pi)/3)# at #theta=(3pi)/4#?
• What is the slope of the tangent line of #r=2theta+3cos((theta)/2-(4pi)/3)# at #theta=(5pi)/4#?
• What is the slope of the tangent line of #r=theta-cos(-4theta+(2pi)/3)# at #theta=(7pi)/4#?
• What is the slope of the tangent line of #r=2theta-cos(5theta+(5pi)/3)# at #theta=(-7pi)/4#?
• What is the slope of the tangent line of #r=2theta-cos(5theta-(2pi)/3)# at #theta=(-7pi)/4#?
• What is the slope of the tangent line of #r=theta^3-thetacos(theta-(pi)/3)# at #theta=(-5pi)/3#?
• What is the slope of the tangent line of #r=2theta^2-3thetacos(2theta-(pi)/3)# at #theta=(-5pi)/3#?
• What is the slope of the tangent line of #r=thetacos(theta/4-(5pi)/3)# at #theta=(-5pi)/3#?
• What is the slope of the tangent line of #r=thetacos(theta/4-(5pi)/3)# at #theta=(pi)/3#?
• What is the slope of the tangent line of #r=thetacos(-3theta+(7pi)/4)# at #theta=(-2pi)/3#?
• What is the slope of the tangent line of #r=theta-cos(4theta-(3pi)/4)# at #theta=(-2pi)/3#?
• What is the slope of the tangent line of #r=theta-cos((4theta)/3-(3pi)/4)# at #theta=(-2pi)/3#?
• What is the slope of the tangent line of #r=theta-3cos((2theta)/3+(pi)/2)# at #theta=(-5pi)/6#?
• What is the slope of the tangent line of #r=5theta+cos(-theta/3-(pi)/2)# at #theta=(-5pi)/6#?
• What is the slope of the tangent line of #r=5theta+cos(-theta/3-(pi)/2)# at #theta=(-pi)/6#?
• What is the slope of the tangent line of #r=-8sin(theta/4)+4cos(theta/2)# at #theta=(2pi)/3#?
• What is the slope of the tangent line of #r=-2sin(3theta)-12cos(theta/2)# at #theta=(-pi)/3#?
• What is the slope of the tangent line of #r=-2sin(2theta)+cos(3theta)# at #theta=(-11pi)/8#?
• What is the slope of the tangent line of #r=12sin(theta/3)*cos(theta/2)# at #theta=(3pi)/2#?
• What is the slope of the tangent line of #r=2sin(theta/4)*cos(theta/2)# at #theta=(9pi)/2#?
• What is the slope of the tangent line of #r=sin(theta/4)/sin(theta/2)# at #theta=(-3pi)/2#?
• What is the slope of the tangent line of #r=(2theta+sin2theta)/cos^2theta# at #theta=(-3pi)/8#?
• What is the slope of the tangent line of #r=(sin^2theta)/(theta-thetacos^2theta)# at #theta=(pi)/4#?
• What is the slope of the tangent line of #r=(sin^2theta)/(-thetacos^2theta)# at #theta=(pi)/4#?
• What is the slope of the tangent line of #r=(sin^2theta)/(2theta-thetacos2theta)# at #theta=(pi)/4#?
• What is the equation of the line that is normal to the polar curve #f(theta)=sintheta-theta/2# at #theta = pi/3#?
• What is the equation of the line that is normal to the polar curve #f(theta)=sin(2theta+pi) -theta# at #theta = pi/4#?
• What is the equation of the line that is normal to the polar curve #f(theta)=2sin(3theta+pi/3) - 2thetacostheta # at #theta = pi/4#?
• What is the equation of the line that is normal to the polar curve #f(theta)= cos(pi-2theta)+thetasin(5theta-pi/2) # at #theta = pi/2#?
• What is the equation of the line that is normal to the polar curve #f(theta)=-5theta- sin((3theta)/2-pi/3)+tan((theta)/2-pi/3) # at #theta = pi#?
• What is the equation of the line that is normal to the polar curve #f(theta)=theta- sin((5theta)/2-pi/2)+tan((2theta)/3-pi/2) # at #theta = pi#?
• What is the equation of the tangent line to the polar curve #f(theta)=theta- sin((3theta)/2-pi/2)+tan((2theta)/3-pi/2) # at #theta = pi#?
• What is the equation of the tangent line to the polar curve # r(theta)=theta^2costheta-theta+sin(theta/3) # at #theta = pi#?
• What is the equation of the tangent line to the polar curve # f(theta)=theta^2costheta-theta+tan(theta/3) # at #theta = pi#?
• What is the equation of the tangent line to the polar curve # f(theta)=theta^2cos(3theta)-thetasin(2theta)+tan(theta/6) # at #theta = pi#?
• What is the equation of the tangent line to the polar curve # f(theta)=2thetasin(theta)+thetacot^2(2theta) # at #theta = pi/8#?
• What is the equation of the tangent line to the polar curve # f(theta)=2thetasin(theta)+thetacot^2(4theta) # at #theta = pi/3#?
• What is the equation of the tangent line to the polar curve # f(theta)= 5thetasin(3theta)+2cot(11theta) # at #theta = pi/12#?
• What is the slope of the polar curve #f(theta) = thetasintheta - cos^3theta + tantheta# at #theta = pi/3#?
• What is the slope of the polar curve #f(theta) = theta^2-theta - cos^3theta + tan^2theta# at #theta = pi/3#?
• What is the slope of the polar curve #f(theta) = theta^2-theta - cos^3theta + tan^2theta# at #theta = pi/4#?
• What is the slope of the polar curve #f(theta) = theta^2-theta - 3sin^2theta + tan^2theta# at #theta = pi/4#?
• What is the slope of the polar curve #f(theta) = -4theta - thetacos^2theta # at #theta = (15pi)/8#?
• What is the slope of the polar curve #f(theta) = theta^2 - thetasintheta # at #theta = (11pi)/8#?
• What is the slope of the polar curve #f(theta) = theta^2 - csctheta # at #theta = (3pi)/4#?
• What is the slope of the polar curve #f(theta) = theta^2 - sectheta # at #theta = (3pi)/4#?
• What is the slope of the polar curve #f(theta) = theta^2 - sec^3theta+tantheta # at #theta = (3pi)/4#?
• What is the slope of the polar curve #r(theta) = theta^2 - sec(theta)+cos(theta)*sin^3(theta) # at #theta = (2pi)/3#?
• What is the slope of the polar curve #f(theta) = theta - sec^2theta+costhetasin^3theta # at #theta = (5pi)/6#?
• What is the slope of the polar curve #f(theta) = theta - sec^2theta+costheta # at #theta = (7pi)/12#?
• What is the slope of the polar curve #f(theta) = theta - sectheta+thetasin^3theta # at #theta = (7pi)/12#?
• What is the slope of the polar curve #f(theta) = theta - sec^3theta+thetasin^3theta # at #theta = (5pi)/8#?
• What is the slope of the polar curve #f(theta) = theta + cot^2theta+thetasin^3theta # at #theta = (3pi)/8#?
• What is the slope of the polar curve #r(theta) = theta + cottheta+thetasin^3theta # at #theta = (3pi)/8#?
• What is the slope of the polar curve #f(theta) = theta + cottheta+thetasin^2theta # at #theta = (3pi)/8#?
• What is the slope of the polar curve #f(theta) = 2theta + tan^2theta - costheta # at #theta = (pi)/8#?
• What is the slope of the polar curve #f(theta) = -theta + sectheta - costheta # at #theta = (5pi)/4#?
• What is the slope of the polar curve #f(theta) = sectheta - csctheta # at #theta = (5pi)/4#?
• What is the slope of the polar curve #f(theta) = sectheta - csctheta # at #theta = (3pi)/4#?
• What is the slope of the polar curve #f(theta) = sectheta - csctheta # at #theta = (3pi)/8#?
• How do you find the points of horizontal tangency of #r=asinthetacos^2theta#?
• How do you find the points of horizontal tangency of #r=3cos2thetasectheta#?
• How do you find the points of horizontal tangency of #r=2csctheta+5#?
• How do you find the points of horizontal tangency of #r=2cos(3theta-2)#?
• How do you sketch the graph of the polar equation and find the tangents at the pole of #r=3sintheta#?
• How do you sketch the graph of the polar equation and find the tangents at the pole of #r=3costheta#?
• How do you sketch the graph of the polar equation and find the tangents at the pole of #r=2(1-sintheta)#?
• How do you sketch the graph of the polar equation and find the tangents at the pole of #r=3(1-costheta)#?
• How do you sketch the graph of the polar equation and find the tangents at the pole of #r=2cos3theta#?
• How do you sketch the graph of the polar equation and find the tangents at the pole of #r=3sin2theta#?
• Question #65a2a
• For the unit vector #hattheta#, geometrically show that #hattheta = -sinthetahati + costhetahatj#? Essentially, converting from cartesian to polar, how would I determine the unit vector for #vectheta# in terms of #theta#, #hati#, and #hatj#?
• A cow is tied to a silo with radius #r# by a rope just long enough to reach the opposite side of the silo. Find the grazing area available for the cow?