find the maximum value of r, any zeros, and state the type of equation r=6+12cosθ

Answer 1

Before you can do this question, you'll need to know that cosine can never give you a number higher than 1 or lower than -1, so 12cosθ can never be more than 12.

So, to find the maximum of r, we can assume cosθ is at its maximum and get r = 6 + 12 = 18

For r to equal 0, 12cosθ would need to equal -6, to cancel out the positive 6.

12cosθ = -6

cosθ = -1/2

cosθ = -1/2 when θ is 120° or 240° (and again at every 360° after these numbers)

Therefor the zeros for r are at 120°+n*360° & 240°+n*360° where n is any integer.

As for what type of equation this is, I'm not quite sure what answer you're looking for. I would call this a sine-wave equation, but I'm sure there are many other names as well.

Hope this helped!