Slope of tangent to polar curve r = 1/θ at θ = π

[Frankenstein19]

Homework Statement

Find the slope of the tangent line to the give polar curve at the point specified by the value of theta R = 1/θ, θ=π

Homework Equations

$\frac{(dr/dθ)sinθ + rcosθ}{(dr/dθ)cosθ - rsinθ}$

The Attempt at a Solution

The derivative of r is -1/θ²

Then plugging things into the formula I get
$\dfrac{\dfrac{-1}{θ^{2}}sinθ +\dfrac{1}{θ}cosθ}{\dfrac{-1}{θ^{2}}cosθ -\dfrac{1}{θ}sinθ}$

then i take out a factor is -1/θ from both the denominator and numerator and get

$\dfrac{\dfrac{sinθ}{θ}+cosθ}{\dfrac{cosθ}{θ}-sinθ}$

then plugging in pi wherever thetha is and doing some math i get that its all equal to pi

the correct answer is supposed to be -pi

what am i doing wrong

 

[Samy_A]

Homework Statement

Find the slope of the tangent line to the give polar curve at the point specified by the value of theta R = 1/θ, θ=π

Homework Equations

$\frac{(dr/dθ)sinθ + rcosθ}{(dr/dθ)cosθ - rsinθ}$

The Attempt at a Solution

The derivative of r is -1/θ²

Then plugging things into the formula I get
$\dfrac{\dfrac{-1}{θ^{2}}sinθ +\dfrac{1}{θ}cosθ}{\dfrac{-1}{θ^{2}}cosθ -\dfrac{1}{θ}sinθ}$

then i take out a factor is -1/θ from both the denominator and numerator and get

$\dfrac{\dfrac{sinθ}{θ}+cosθ}{\dfrac{cosθ}{θ}-sinθ}$

then plugging in pi wherever thetha is and doing some math i get that its all equal to pi

the correct answer is supposed to be -pi

what am i doing wrong

Check the signs after the step "then i take out a factor is -1/θ from both the denominator and numerator and get"