If cosecθ = \sqrt{10} then sec θ = ?

Foundation

Mathematics Foundation

Introduction to Trigonometry

Question

If $cosecθ = \sqrt{10}$ then sec θ = ?

$\frac{\sqrt{10}}{3}$

$\frac{2}{\sqrt{10}}$

$\frac{1}{\sqrt{10}}$

$\frac{3}{\sqrt{10}}$

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Given cosec θ = √10, we know sin θ = 1/√10. Using the identity sin²θ + cos²θ = 1, we find cos²θ = 1 - sin²θ = 1 - (1/10) = 9/10. Therefore, cos θ = 3/√10 (taking positive root for acute angle). Finally, sec θ = 1/cos θ = √10/3.

Final answer: $\frac{\sqrt{10}}{3}$