If sin θ = 12/13 and θ ∈ (0, πover2 ), then what is the value of tanθ?

If sin θ = 12/13 and θ ∈ (0, πover2 ), then what is the…

If sin $\theta$ = $\frac{12}{13}$ and θ ∈ (0, $\pi\over2$ ), then what is the value of tanθ?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. $12\over5$ .

sinθ = 12/13

⇒ sin²θ = 144/169

⇒ cosθ = √(1 – sin²θ) = √(1 – 144/169) = √(25/169) = 5/13

⇒ tanθ = sinθ/cosθ = (12/13)/(5/13) = 12/5