Question

Find the polar tangencies of ( r = sin(3θ) ) from ( 0 ) to ( 2π ).

a) ( θ = 0, π/6, 5π/6, π, 7π/6, 11π/6, 2π )
b) ( θ = π/3, π/2, 2π/3, 4π/3, 3π/2, 5π/3 )
c) ( θ = π/4, 3π/4, 5π/4, 7π/4 )
d) ( θ = π/2, 3π/2 )

Answer 1

The polar tangencies of the equation r = sin(3θ) are θ = 0, π/3, 2π/3, π, 4π/3, 5π/3.

Step-by-step explanation:

The polar tangencies of the equation r = sin(3θ) can be found by finding the values of θ that make the equation equal to zero.

Setting r = sin(3θ) equal to zero, we get sin(3θ) = 0. Since the sine function is zero at multiples of π, we can solve for θ by setting 3θ equal to π times an integer:

• 3θ = 0, π, 2π, 3π, ...

By dividing each equation by 3, we find the values of θ that satisfy the given equation: θ = 0, π/3, 2π/3, π, 4π/3, 5π/3.