How do you graph $r = 2 sin (θ) + 2 cos (θ)$ $r = 2 sin(theta) + 2 cos(theta)$ ?

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How do you graph $r = 2 sin (θ) + 2 cos (θ)$ $r = 2 sin(theta) + 2 cos(theta)$ ?

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Answer 1 · 2016-05-18T11:45:47

The graph is the circle of radius $\sqrt{2}$ $sqrt 2$ and center at $(\sqrt{2}, \frac{π}{4})$ $(sqrt 2, pi/4)$ The pole is on the circle. The circle coordinates for the pole are $(0, - \frac{π}{4})$ $(0, -pi/4)$ .

Explanation:

The given equation can be condensed to

$r = 2 \sqrt{2} sin (θ + \frac{π}{4})$ $r=2sqrt 2 sin (theta+pi/4)$ ,

using $sin (θ + \frac{π}{4})$ $sin (theta+pi/4)$

$= sin θ cos (\frac{π}{4}) + cos θ sin (\frac{π}{4})$ $=sin theta cos (pi/4)+cos theta sin (pi/4)$

$= (\frac{1}{\sqrt{2}}) (sin θ + cos θ)$ $=(1/sqrt 2)(sin theta+cos theta)$

Any equation of the form

$r = d cos (θ + α)$ $r = d cos (theta + alpha)$ or

$r = d sin (θ + α)$ $r = d sin (theta + alpha)$ represents a circle with diameter and

center at #(d/2, +-alpha).

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How do you graph $r = 2 sin (θ) + 2 cos (θ)$ $r = 2 sin(theta) + 2 cos(theta)$ ?

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Explanation:

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