Applying criteria of symmetry, graph?

Question

Can you help me solve this please May 5 stars

Applying criteria of symmetry, graph r = 6 (1 + cos (Θ + α))

for

a) α = 0

b) α = Π / 4

c) α = Π / 2

use the graph to describe the effect of the angle α

enter the equation as a function of Θ sen to paragraph c)

Answer 1

Respuesta preferida

you do know that r = 1 + cos Θ is a cardioid with no inner loop..passing through ( 2 , 0 ) , (1,π / 2 ),

and (0, π )...r = 6 ( 1 + cos Θ) just increases the r value by a multiple of 6...

r = 6 ( 1 + cos (Θ + Φ ) ) is a rotation clockwise of angle Φ , ie . if Θ = - Φ then the point ( 112 , - Φ)

corresponds to ( 12 , 0 ) of r = 6 (1 + cos Θ)...thus α = π / 4 means a clockwise rotation of π / 4 radians