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Given the equation of a circle
Find the new equation of a circle if the given circle is rotated counterclockwise about the origin at 30°.
Solution:
The first thing that we need to do is to write the given equation in standard form as follows
From the standard form, we can draw the circle as follows
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| Photo by Math Principles in Everyday Life |
If the given equation is written in rectangular coordinate system, then we need to convert it into polar coordinate system as follows
Next, substitute θ with θ - 30° and then expand using the sum and difference of two angles formula, we have
Convert the above equation into rectangular coordinate system in order to get its final equation. Therefore, the new equation of a circle is
