# calculus

posted by .

For what values of theta, on the polar curve r=theta, 0<=theta<=2pi, are there horizontal tangent curves? Vertical?

I got one answer for the horizontal tangent. and it's theta = 0 but what are the other ones?/

• calculus -

since r = θ

x = r cosθ
y = r sinθ

dy/dθ = r' sinθ + r cosθ = sinθ + θcosθ
dx/dθ = r' cosθ - r sinθ = cosθ - θsinθ

dy/dx = (sinθ + θcosθ)/(cosθ - θsinθ)

You are correct that dy/dx = 0 when θ=0
It is also zero when x = 2.04 and 4.88
(approximately)

The tangent is vertical when the denominator is zero: x = 0.84 and 3.45

## Similar Questions

1. ### calculus

for what value of r=4sinè have vertical tangent?
2. ### physics

A ball is attached to a string with length of L. It swings in a horizontal circle, with a constant speed. The string makes an angle (theta) with the vertical, and T is the magnitude of the tension in the string. 1)Determine the Mass …
3. ### Calculus

I wanted to confirm that I solved these problems correctly (we had to convert the polar curves to Cartesian equations). 1.rcos(theta)=1 x=1 2.r=2*sin(theta)+2*cos(theta) r^2=2rsin(theta)+2rcos(theta) x^2+y^2=2y+2x (a little unsure …
4. ### Advanced Math

Identify the polar form of the linear equation 4x+3y=10. x=rcos(theta),y=rsin(theta) 4x+3y=4rcos(theta)+3rsin(theta)=10 r=10/(4cos(theta)+3sin(theta) I got it wrong
5. ### calculus

For what values of theta, on the polar curve r=theta, 0<=theta<=2pi, are there horizontal tangent curves?
6. ### trig

If cosecant of theta equals 3 and cosine of theta is less than zero, find sine of theta, cosine of theta, tangent of theta, cotangent of theta and secant of theta
7. ### 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= …
8. ### calculus

Find circumference of the circle r=2acos theta. s= Int (0 to 2pi) of Sqrt(4a^2cos^2 theta+4a^2sin^2 theta)d theta =Int (0 to 2pi)2a*Int theta d theta =2a(2pi-0)=4a*pi Book shows 2a*pi. Am I wrong somewhere?