The graph of a limacon curve is given. Without using your graphing calculator, determine which equation is correct for the graph. [-5, 5] by [-5, 5]. a. r= 2-2 sinθ b. r= 3-2 sinθc. r= 2+2 sinθd. r= 1-3 sinθ

Answer:The equation of the limacon is r = 2 - 2 sinФ ⇒ answer (a)Step-by-step explanation:* Lets study the limacon curve- Equations of the form:# r = a + b sin θ# r = a – b sin θ# r = a + b cos θ# r = a – b cos θ All will produce limacons.  * Lets examine what happens for various values of a and b.- When the value of a is less than the value of b, the graph is  a limacon with and inner loop.  ⇒ figure (1)- When the value of a is greater than the value of b, the graph is  a dimpled limacon.  ⇒ figure (2)- When the value of a is greater than or equal to the value of 2b,  the graph is a convex limacon.  ⇒ figure (3)- When the value of a equals the value of b, the graph is a special  case of the limacon.  It is called a cardioid.  ⇒ figure (4)* Notice that, in each of the graphs of the liamsons, changing  from sine to cosine does not affect the shape of the graph just its  orientation.  - Equations using sine will be symmetric to the vertical axis- Equations using cosine are symmetric to the horizontal axis.* The sign of b will also affect their orientation.- The large of the graph under the x-axis or left to the y-axis b is -ve- The large of the graph over the x-axis or right to the y-axis b is +ve* lets look to the graph∵ The graph is symmetric to the y- axis∵ The graph is a cardioid∴ a = b∵ The large part of the graph under the x-axis∴ b is -ve∴ The answer is r = 2 - 2 sinФ* The equation of the limacon is r = 2 - 2 sinФ