Determining the Slope and Tangent Lines for a Polar Curve
Determining the slope and tangent lines for a polar curve is a fundamental concept in calculus that allows for the analysis of curves defined by polar coordinates. In polar coordinates, points on a plane are represented by their distance from the origin (radius) and the angle they make with the positive x-axis (polar angle). Understanding how to calculate the slope of a polar curve at a given point and finding tangent lines enables mathematicians to explore the behavior and characteristics of these curves in various contexts, from physics to engineering and beyond.
Questions
- 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=2cos(theta-pi/2) + sin(2theta-pi)# at #theta=pi/4#?
- How do you find the points of horizontal tangency of #r=asinthetacos^2theta#?
- What is the slope of the tangent line of #r=(2theta+sin2theta)/cos^2theta# at #theta=(-3pi)/8#?
- What is the slope of the polar curve #f(theta) = theta^2 - sectheta # at #theta = (3pi)/4#?
- What is the slope of the tangent line of #r=-2sin(3theta)-12cos(theta/2)# at #theta=(-pi)/3#?
- 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#?
- How do you find the slope of a polar curve?
- 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=cos(theta+pi/2)*cos(theta-pi) # at #theta=(-pi)/8#?
- How do you find the slope of the polar curve #r=3+8sin(theta)# at #theta=pi/6# ?
- What is the equation of the tangent line of #r=5theta + 2sin(4theta+(2pi)/3) # at #theta=(2pi)/3#?
- What is the slope of the polar curve #f(theta) = theta - sectheta+thetasin^3theta # at #theta = (7pi)/12#?
- How do you find the slope of the polar curve #r=cos(2theta)# at #theta=pi/2# ?
- What is the slope of the tangent line of #r=theta/3+sin((3theta)/8-(5pi)/3)# at #theta=(7pi)/6#?
- What is the equation of the tangent line of #r=cos(theta+(5pi)/4) * sin(theta-(17pi)/12)# at #theta=(-5pi)/12#?
- The tangent to #y=x^2e^x# at #x=1# cuts the #x# and #y#-axes at #A# and #B# respectively. Find the coordinates of #A# and #B#.?
- What is the slope of the polar curve #r(theta) = theta + cottheta+thetasin^3theta # at #theta = (3pi)/8#?
- 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 polar curve #f(theta) = thetasintheta - cos^3theta + tantheta# at #theta = pi/3#?