Determine the maximum r-value of the polar equation r= 3+3 cos theta

Step-by-step explanation:

Hi there,

To get started, recall that the cosθ of an angle has a definite maximum value, which is:

   Hence the cosine of any angle can never be greater than 1, which is illustrated if you plot the graph of cos(x) on a graphing calculator or Desmos.com. Thus, 1 is the maximum of cosθ; the same goes for sinθ, but at a different angle.

With this in mind, plug this in:

Therefore, the maximum r-value from this polar equation is 6.

If you are adept in calculus, this equation can also be solved using a derivative and some trigonometry:

In calculus, the maximum of a function is when its rate is equal to zero:

Sine of a RADIANS angle is only equal to zero when θ is equal to the following:

     where n=0,1,2,3,...  and π is in radians

Hence plug in 0 into the original equation for θ to make cosine a maximum:

r=3 + 3(cos0) = 3 +3(1) = 6

Same answer obtained!

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