Home > APCALC > Chapter 11 > Lesson 11.3.1 > Problem11-80

11-80.

Write the equation of the line tangent to the polar curve $r = -1 + \cos(θ) \text{ at } θ =\frac { \pi } { 2 }$.

To write the equation of the line, the slope, or $dy/dx$ is needed.

For the given value of $θ$, where is the point on the curve?
What are the coordinates of this point in rectangular form?

$x=r\cos(\theta)=(-1+\cos(\theta))(\cos(\theta))$

$y=r\sin(\theta)=(-1+\cos(\theta))(\sin(\theta))$

Write an equation for:

$\frac{dy}{dx}=\frac{\frac{dy}{d\theta}}{\frac{dx}{d\theta}}$

Evaluate your slope equation from Step 3 using the (rectangular) point $\left(0, –1\right)$.