Question

To find all points of intersection between the curves r=8sin(2θ) and r=4, you would set the two equations equal to each other and solve for θ.

Answer 1

To find the points of intersection, set the two equations equal to each other and solve for θ. The solutions are approximately θ = 0.262 radians and θ = 0.879 radians.

Step-by-step explanation:

To find the points of intersection, we need to set the two equations equal to each other and solve for θ.

Equation 1: r = 8sin(2θ)

Equation 2: r = 4

Setting these two equations equal to each other, we have: 8sin(2θ) = 4

Divide both sides by 8: sin(2θ) = 0.5

Now we need to find the values of θ that satisfy this equation. Since sin is a periodic function, we can use the inverse sine function to find the solutions.

Using the inverse sine function, we have: 2θ = arcsin(0.5)

θ = arcsin(0.5)/2

By evaluating this expression, we find that θ ≈ 0.262 radians and θ ≈ 0.879 radians.

Therefore, the points of intersection between the two curves occur at θ ≈ 0.262 radians and θ ≈ 0.879 radians.