# Determining the Slope and Tangent Lines for a Polar Curve - Page 5

Questions

- What is the slope of the tangent line of #r=theta^3-thetacos(theta-(pi)/3)# at #theta=(-5pi)/3#?
- What is the equation of the tangent line of #r=theta-3sin(theta+(5pi)/3) # at #theta=(2pi)/3#?
- What is the slope of the polar curve #f(theta) = theta - sec^2theta+costheta # at #theta = (7pi)/12#?
- What is the equation of the tangent line to the polar curve # f(theta)=2thetasin(theta)+thetacot^2(2theta) # at #theta = pi/8#?
- 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#?
- What is the slope of the tangent line of #r=2theta-3sin((13theta)/8-(5pi)/3)# at #theta=(7pi)/6#?
- What is the equation of the tangent line of #r=cos(-3theta-(2pi)/3) # at #theta=(-5pi)/3#?
- How do you sketch the graph of the polar equation and find the tangents at the pole of #r=2cos3theta#?
- 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 #r=sintheta# at #theta=pi#?
- 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^2-theta - 3sin^2theta + tan^2theta# at #theta = pi/4#?
- Find the points where tangents to #cotx in [0, pi]# are parallel to the line #y = -2x+3# ?
- What is the slope of the tangent line of #r=3sin(theta/2-pi/4)# 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 slope of the tangent line of #r=-8sin(theta/4)+4cos(theta/2)# at #theta=(2pi)/3#?
- How do you find the points of horizontal tangency of #r=3cos2thetasectheta#?
- What is the slope of the polar curve #f(theta) = theta - sec^2theta+costhetasin^3theta # at #theta = (5pi)/6#?
- What is the equation of the tangent line of #r=2cos(theta-pi/2) - sin(2theta-pi)# at #theta=pi/4#?
- What is the slope of the tangent line of #r=2theta-cos(5theta-(2pi)/3)# at #theta=(-7pi)/4#?