Suppose that x = 4tan(θ). What is the value of sin(θ)
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Suppose that x = 4tan(θ). What is the value of sin(θ)

[From: ] [author: ] [Date: 12-01-27] [Hit: ]
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So I switched tan for Sin(θ)/Cos(θ) but I still don't get what to do. Can someone help?

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tanΘ = x/4 = sinΘ/cosΘ

Square both sides:
tanΘ = sin²Θ/cos²Θ

Use the Pythagorean Identity, cos²Θ + sin²Θ = 1
tan²Θ = sin²Θ/(1-sin²Θ)

tan²Θ(1-sin²Θ) = sin²Θ
tan²Θ = (1+tan²Θ)sin²Θ

sin²Θ = tan²Θ/(1+tan²Θ)
sinΘ = ±tanΘ/√(1+tan²Θ)

sinΘ = ±(x/4)/√(1+x²/16)
= ± x/√(x²+16) : The sign of sinΘ cannot be determined from the information given.

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x = 4tan(θ).
tan(θ) = x/ 4
sec(θ) = Sqart( 1 - tan^2(θ) )
=Sqrt(1 - x^2/4)
= Sqrt(4-x^2)/2
cos(θ) = 2/Sqrt(4-x^2)
Sin(θ) = 1 - Cos^2(θ)
Plug the value of cos(θ) there

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x = 4tan(θ)

sin(θ) =+/- x/√(x² + 16)
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