## Related questions with answers

Question

Find the polar equation of the tine tangent to the polar curve $r=\cos \theta+\sin \theta$ at the origin, and then find the slope of this tangent line.

Solution

VerifiedStep 1

1 of 2To find the equation of the line tangent to the polar curve $r=\cos \theta+\sin \theta$ at the origin we need to solve the equation $r=0$ for $\theta$:

$\begin{align*} r&=0\Leftrightarrow\\ \cos \theta&=-\sin \theta\Leftrightarrow\\ \cos (-\theta)&=\sin (-\theta)\Leftrightarrow\\ -\theta&=\frac{\pi}{4}\Leftrightarrow \pmb{\theta=-\frac{\pi}{4}\,\,\lor \,\, \theta=\frac{3\pi}{4}} \end{align*}$

Now that we know that the equation of the tangent line at the origin is $-\frac{\pi}{4}$ we see that the slope of the line is equal to

$\boxed{\tan \left( -\frac{\pi}{4}\right)=-1}$

## Create a free account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Create a free account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Recommended textbook solutions

#### Thomas' Calculus

14th Edition•ISBN: 9780134438986 (11 more)Christopher E Heil, Joel R. Hass, Maurice D. Weir10,142 solutions

#### Calculus: Early Transcendentals

3rd Edition•ISBN: 9780134763644 (5 more)Bernard Gillett, Eric Schulz, Lyle Cochran, William L. Briggs13,437 solutions

#### Calculus: Early Transcendentals

8th Edition•ISBN: 9781285741550 (6 more)James Stewart11,084 solutions

#### Calculus: Early Transcendentals

9th Edition•ISBN: 9781337613927 (1 more)Daniel K. Clegg, James Stewart, Saleem Watson11,050 solutions

## More related questions

1/4

1/7