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Calculus help please and thank you

Calculus help please and thank you-example-1
User Federom
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Since π ≤ θ ≤ 2π (meaning θ is an angle that terminates in either the 3rd or 4th quadrant), we know that sin(θ) < 0.

Recall the Pythagorean identity,

sin²(θ) + cos²(θ) = 1

so that

sin(θ) = -√(1 - cos²(θ)) = -√(1 - (3/4)²) = -√7/4

By definition of tangent,

tan(θ) = sin(θ)/cos(θ) = (-√7/4)/(3/4) = -√7/3

Recall the double angle identity for sine:

sin(2θ) = 2 sin(θ) cos(θ) = 2 (-√7/4) (3/4) = -3√7/8

User Alxyzc
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