Polar+Functions+(BC)



==Polar equations are derived from polar coordinates, p, of the form (r, theta), given an initial ray with endpoint as the origin and where r is the radius and theta is the angle the radius makes with the given ray.==

As the coefficient of cosine changes the inner part of the circle either gets smaller larger or non existent.
In polar equations their graphs sometimes have s series of curves, called rose petals.

When **//k//** = 1 there is one petal. As you see, when **//k//** = n we will have n petals
Ex.) 1 + cos (2 * theta)

Ex.)
Convert the rectangular equation //y//2 = //x//3 to polar equation. A. r = tan2 //θ// sec //θ// B. r = tan2 //θ// C. r2 = tan2 //θ// sec //θ// D. r = cot2 //θ// cos //θ//
 * Choices:**
 * Correct Answer: A**
 * Solution:**
 * Step 1:** //y2// = //x//3 [Rectangular equation.]
 * Step 2:** (//r//sin //θ//)2 = (//r//cos //θ//)3 [Use //y// = //r//sin //θ// and //x// = //r//cos //θ//]
 * Step 3:** //r2//sin2 //θ// = //r//3cos3 //θ//
 * Step 4:** sin2 //θ// / cos3 //θ// = //r//3/ //r//2
 * Step 5:** //r// = tan2 //θ// sec //θ//
 * Step 6:** So, the polar equation is //r// = tan2 //θ// sec //θ//.


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