How do you graph $r=-2sintheta$ ?

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Answer 1 · 2016-10-14T19:02:10

The way that you graph this is, set your compass to a radius of 1, put the center point at $(0, -1)$ , and draw a circle.

Multiply both sides by r:

$r^2 = -2rsin(theta)$

Substitute $x^2 + y^2$ for $r^2$ and $y$ for $rsin(theta)$

$x^2 + y^2 = -2y$

Write $x^2 as (x - 0)^2$ :

$(x - 0)^2 + y^2 = -2y$

Add $2y + k^2$ to both sides:

$(x - 0)^2 + y^2 + 2y + k^2= k^2$

Using the pattern $(y - k)^2 = x^2 - 2ky + k^2$ we observe that we can use the 2y term to find the value of $k and k^2$ :

$-2ky = 2y$

$k = -1 and k^2 = 1$

Substitute this into the equation:

$(x - 0)^2 + y^2 + 2y + 1= 1$

This means y terms on the left side can be written as $(y - -1)^2$ :

$(x - 0)^2 + (y - -1)^2 = 1^2$

The way that you graph this is, set your compass to a radius of 1, put the center point at $(0, -1)$ , and draw a circle.

How do you graph r=-2sinthetar=-2sintheta?