Answer:
The equation r = 3 - cos Ф is correct for the graph ⇒ 3rd answer
Step-by-step explanation:
Equations of the form r = a + b sin Ф, r = a - b sin Ф, r = a + b cos Ф, and r = a - b cos Ф represent limacons
- Equations r = a + b sin Ф, r = a - b sin Ф are symmetric to the vertical axis
- Equations r = a + b cos Ф, r = a - b cos Ф are symmetric to the horizontal axis
- The shape of the limacons depends on the values of a and b
∵ The figure is a circle
- That means a is greater than twice b
∴ a > 2b
∵ The circle is symmetric to the x axis
∵ The majority of the circle lies in quadrants two and three
- That means most of the graph at the negative part of x
∴ The form of the equation is r = a - b cos Ф
Lets look to the answer to find the right one
∵ a > 2b
∴ a = 3 and b = 1 because 3 > 2(1)
∴ The answer is r = 3 - cos Ф
The equation r = 3 - cos Ф is correct for the graph
