Given that cosθ 1/3 and θ is acute, what is tanθ?

Question

Mathematics

William Hood

9 March, 09:41

Given that cosθ 1/3 and θ is acute, what is tanθ?

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Answers (1)

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Peter Sullivan · Answer 1

tanθ=2√2

Step-by-step explanation:

cosθ = 1/3, and θ is acute;

cos²θ=1/9

sin²θ+cos²θ=1

sin²θ=1-cos²θ=1-1/9=8/9

=> sinθ=√ (8/9) = 2√2 / 3

tanθ=sinθ/cosθ

tanθ = (2√2 / 3) / (1/3) = 2√2

tanθ=2√2