How to graph equations by plotting points with the form like r = -cos θ

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Welcome to graphing polar equations by plotting points. Today we'll learn how to graph the equation r equals negative cosine theta. This method involves choosing specific angle values, calculating the corresponding r values, and then plotting these polar coordinates on a polar grid. Let's create a value table for r equals negative cosine theta. We'll choose common angle values from 0 to 2 pi and calculate the corresponding r values. Notice that when cosine is positive, r becomes negative, and when cosine is negative, r becomes positive. Understanding negative radius values is crucial. When r is negative, we don't plot the point at the given angle. Instead, we plot it in the opposite direction. For example, if theta equals 0 degrees and r equals negative 1, we plot the point at distance 1 in the opposite direction, which is at 180 degrees. Here's the complete graph of r equals negative cosine theta. By plotting all the points and connecting them with a smooth curve, we get a circle! This might be surprising, but it demonstrates the beauty of polar coordinates. The curve passes through the origin and has a maximum distance of 1 from the origin. This type of systematic point plotting is essential for understanding polar equations. Let's create a value table for r equals negative cosine theta. We'll choose common angle values from 0 to 2 pi and calculate the corresponding r values. Notice that when cosine is positive, r becomes negative, and when cosine is negative, r becomes positive.