Answer: Correct answer is pie/2 or A
Explanation:
r = -5sinθ + 4θ has symmetry with respect to the line θ = π/2.
To demonstrate this, we can apply the third symmetry test for polar equations:
Symmetry with respect to the line θ = π/2: Replace θ by π - θ and see if the equation remains the same. If it does, the equation has symmetry with respect to the line θ = π/2.
r = -5sin(π/2 - θ) + 4(π/2 - θ) = 5cosθ + 2π - 4θ
r = 5cosθ + 2π - 4θ is the same as the original equation, so there is symmetry with respect to the line θ = π/2.
Therefore, the correct answer is θ = π/2.