How do you graph polar coordinates?
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To graph polar coordinates, we use the polar coordinate system, which is based on a circle. In this system, each point is determined by a distance from the origin (called the radius, denoted by (r)) and an angle from the positive xaxis (called the angle, denoted by (\theta)).

Plotting Points: To plot a point given in polar coordinates ((r, \theta)), start at the origin, move along the polar axis (positive xaxis) to a distance of (r) units, and then rotate counterclockwise by an angle of (\theta) degrees.

Special Cases:
 If (r) is negative, it means the point is on the opposite side of the origin but still at the same angle (\theta).
 If (\theta) is negative, it means rotating clockwise instead of counterclockwise.

Graphing Curves: To graph curves given in polar coordinates, such as (r = f(\theta)), where (f(\theta)) is some function of (\theta), you can plot points by choosing different values of (\theta) and calculating the corresponding (r) values. Connecting these points will give you the graph of the curve.

Examples:
 To graph a circle with radius (r), you would plot points ((r, \theta)) for all values of (\theta) from 0 to (2\pi).
 To graph a line through the origin at an angle (\theta), you would plot points ((r, \theta)) where (r) varies.

Conversion: To convert polar coordinates to Cartesian coordinates, you can use the formulas (x = r \cdot \cos(\theta)) and (y = r \cdot \sin(\theta)).
Overall, graphing polar coordinates involves understanding the relationship between the radius and angle and using this information to plot points and graph curves.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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