Question

Find the slope of the tangent line to the polar curve r=2sin(theta) for the given value (theta)=(pi/6).

Answer 1

\[dy/dx= (rcos \theta+\sin \theta *dr/d \theta)/(-rsin \theta+\cos \theta*dr/d \theta)\]
This is the equation we're supposed to use, and when I try it, ut works out to:
\[\sqrt{3}+3\]
But the answer is supposed to be:
\[\sqrt{3}\]

I'm not sure what I'm doing wrong becuase I've checked my work and nothing looks wrong.

Answer 2

Please show your result for \(\dfrac{dr}{d\theta}\).

Answer 3

\[dr/d \theta=2\cos\]

Answer 4

*2cos(theta)

Answer 5

Right. I was going to call you out on that! Good work beating me to it.

Answer 6

Typos, haha. Sorry about that.

Answer 7

How did you proceed after that? Did you use 'r' in the giant fraction or \(2\sin(\theta)\)?

Answer 8

I used 2sin(theta)

Answer 9

Okay, so Numerator

\(4\sin(\theta)\cos(\theta)\)

How did that go?

Answer 10

How did you get that? I got \[(2\sin \theta)\cos \theta+\sin \theta(2\cos \theta)\]

Answer 11

nevermind, you simplified, right?

Answer 12

Then for the denominator
\[-(2\sin \theta)\sin \theta+\cos \theta(2\cos \theta)\] ?

Answer 13

@tkhunny ?

Answer 14

Couldn't find the thread. Not sure why. I'm back.

That's it. Now, use your best trigonometry to change to functions of \(2\theta\).