Barrons AP Calculus

(Marvins-Underground-K-12) #1

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BC  ONLY

Example 17 __

Consider the polar function r = 2 + 4 sin θ.


For what    values  of  θ   in  the interval    [0,2π]  does    the curve   pass    through the
origin?
For what value of θ in the interval [0, π/2] does the curve intersect the circle
r = 3?

SOLUTION:


At  the origin  r   =   0,  so  we  want    2   +   4   sin θ   =   0.  Solving for θ   yields  sin 
which occurs at and .
The curves r = 2 + 4 sin θ and r = 3 intersect when 2 + 4 sin θ = 3, or sin

. From the calculator we find .

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