# calculus

for what value of r=4sinè have vertical tangent?

In polar coordinates? Theta=90 deg is vertical.

I do not know if you know how to differentiate polar coordinate equations so I changed your equation from polar to rectangular form, I don't know if that is the way you do it.

anyway I got x^2 + y^2 = 4y which is the equation of a circle.

I differentiated that

2x + 2y(dy/dt) = 4dy/dt
.
.
dy/dt = -x/(y-2)

for the tangent to be a vertical line, its slope must be undefined.
This happens when the denominator is 0
so y-2=0
y=2
then substitute that in the equation for x=2
so in Cartesian form the point is (2,2), making an angle of 45º or pi/4 radians.

in polar form (r,theta) it would be (√8,pi/4)

1. 👍 0
2. 👎 0
3. 👁 188

## Similar Questions

1. ### calculus

For what values of theta, on the polar curve r=theta, 0

asked by Anonymous on November 2, 2011
2. ### calculus

For what values of theta, on the polar curve r=theta, 0

asked by Anonymous on November 2, 2011
3. ### Calculus

Convert the polar equation to rectangular coordinates: r = 2-cos theta ...and find all points of vertical and horizontal tangency.

asked by Liz on April 16, 2013
4. ### Math

Given any Cartesian coordinates, (x,y), there are polar coordinates (r, theta) with -pi/2 < theta

asked by Kid on September 26, 2019
5. ### Math (Calculus)

Given any Cartesian coordinates, (x,y), there are polar coordinates (r,theta) with –pi/2< theta < pi/2. Find polar coordinates with –pi/2 < theta < pi/2 for the following Cartesian coordinate: If (x,y) = (11,–7) then (r,

asked by Amy on June 2, 2011
6. ### Calculus

Use the given equation to answer the following questions. (Enter your answers from smallest to largest.) r = 8cos(¦È) 0 ¡Ü ¦È < ¦Ð (a) Find the points on the given curve where the tangent line is horizontal. theta= theta=

asked by Cynthia on June 1, 2012
7. ### Precal

How do you find range of theta values for a polar equation? Usually the range of theta is 0 to 2 pi radians (or 0 to 360 degrees). It could be defined for a wider range of angle, but 2 N pi + theta, with N any integer, is

asked by hksda on March 21, 2007
8. ### Precal

The point (r,theta) in polar coordinates is (7,5) in rectangular coordinates. What is the point (2r, theta + pi/2) in rectangular coordinates? So I tried this problem and got r = sqrt(74). But while finding the value of theta, I

asked by Dave on August 9, 2014