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Misha Larkins [42]
3 years ago
11

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

9" id="TexFormula1" title="1/16v^2sin(theta)cos(theta)" alt="1/16v^2sin(theta)cos(theta)" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Artist 52 [7]3 years ago
7 0

Answer:

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

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