Tangent slope with polar coordinate

1. Mar 13, 2017

yecko

1. The problem statement, all variables and given/known data
http://i.imgur.com/4FPnTNS.jpg

2. Relevant equations
(Written in above photo)

3. The attempt at a solution
(Written in above photo)

I have tried hard in figuring out what's wong I have done done, but what I finally got is still option d instead of the model answer e.
Are there any bugs and where are they?
Thank you very much.

(Please forgive me for writing out all the thing because of the difficulty in typing all those expressions.)

2. Mar 13, 2017

BvU

How much is $-{1\over 2} -{1\over 2}$ ?

3. Mar 13, 2017

yecko

It is -1 which I forgot to change in the last line of the step, but I have corrected it in the following steps already... It shouldn't be a problem to the answer...

Whats other bug? thank you.

4. Mar 13, 2017

ehild

Try to draw the curve r=f(θ). Is θ=pi/4 in the domain?

Attached Files:

• r(theta).jpg
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5. Mar 13, 2017

BvU

No you haven't.

6. Mar 13, 2017

BvU

[EDIT]Typo. I see what you mean -- and what the exercise composer means

Attached Files:

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7. Mar 13, 2017

ehild

The polar coordinate r can not be negative as it is the distance from the origin.Half of your curve resulted from negative r=f(θ). The problem maker forgot about that.

Last edited: Mar 13, 2017
8. Mar 14, 2017

John Park

(Edit)
Unless I blundered, it looks quite tractable if you start by transforming to cartesian co-ordinates.

Edit: I did and it isn't

Last edited: Mar 14, 2017