Use a double angle identity to rewrite the formula r(Θ)=

1/32v²sin2θ

Step-by-step explanation:

Given the expression r(theta) = 1/16v²sinθcosθ

According to double angle of trigonometry identity;

Sin2θ = sin(θ+θ)

Sin2θ = sinθcosθ + cosθsinθ

Sin2θ = 2sinθcosθ

sinθcosθ = sin2θ/2 ... **

Substituting equation ** into the question

1/16v²sinθcosθ = 1/16v²(sin2θ/2)

1/16v²sinθcosθ = 1/2×1/16v²(sin2θ)

1/16v²sinθcosθ = 1/32v²sin2θ

Hence using the double angle identity, the equivalent expression is 1/32v²sin2θ

452,489 to the nearest thousand is 452,000