Question

So I'm currently trying to find the points where the tangent line is horizontal of this Eq.
\(r=6+cos(\Theta\))

So from that, I get: \[dy/d \Theta = -\sin^2(\theta)+6\cos(\theta)+\cos^2(\theta) = 0\]

How do I solve for theta first, then find the points? I honestly don't know where to start

Answer 1

You can solve for theta by factoring

Answer 2

Where do I start from there?

Answer 3

Do you need help factoring?

Answer 4

Yeah, I do.

Answer 5

You can use double angle to simpify yout cos^2(theta) - sin^2(theta)

Answer 6

So then you have cos2theta + 6costheta

Answer 7

How do you solve for zero from there?

Answer 8

I have to go, take a look at this: http://www.purplemath.com/modules/solvtrig.htm

Answer 9

How do you know anything about a tangent line if a tangent line doesn't exist? You'll need the denominator, too.

Answer 10

where do you get your fancy derivative ?
this is just a cos wave the tangent is at max/min

Answer 11

pushed up 6 so 7 max 5 min

Answer 12

.

Answer 13

@jamaica25 Actually, as this is an equation in Polar Coordinates, it's quite a bit different. Watch and learn.