The type of limacon graphed by the polar equation r = 4 + 2sin(theta) is a cardioid. The axis of symmetry is the polar axis (theta = 0) and the polar axis (theta = pi) since the equation is symmetrical around these angles.
To find the horizontal and vertical intercepts, we need to set r equal to zero:
0 = 4 + 2sin(theta)
-2 = sin(theta)
Since sine can only take values between -1 and 1, there are no solutions for theta that satisfy this equation. Therefore, there are no horizontal or vertical intercepts for this particular polar equation.
What type of limacon is graphed by the polar equation r=4+2 sin theta? Identify the axis of symmetry and horizontal and vertical intercepts.
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