# How do you graph #r=4sintheta-2#?

See explanation.

A Table for making one half of the graph:

I have inserted graph for the cartesian double

equivalent.

For the given polar equation, the graph would be the inner

loop only. Please feel such nuances while making graphs, when you

make conversions..

graph{x^4+y^4-8y^3+2x^2y^2-8x^2y+12y^2-4x^2=0 [-10, 10, -5, 5]}

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To graph ( r = 4\sin(\theta) - 2 ), follow these steps:

- Plot the initial value of ( r ) when ( \theta = 0 ). Substitute ( \theta = 0 ) into the equation to find ( r ). In this case, ( r = 4\sin(0) - 2 = 0 - 2 = -2 ).
- Plot the point (0, -2) on the polar coordinate plane.
- Determine the behavior of the graph by analyzing the equation. Since ( \sin(\theta) ) ranges from -1 to 1, ( r ) will vary between ( 4(-1) - 2 = -6 ) and ( 4(1) - 2 = 2 ).
- Plot additional points by choosing different values of ( \theta ), such as ( \theta = \frac{\pi}{6} ), ( \theta = \frac{\pi}{4} ), ( \theta = \frac{\pi}{3} ), and so on, and calculating the corresponding ( r ) values using the equation.
- Connect the plotted points to form the graph of ( r = 4\sin(\theta) - 2 ).

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