If tanθ = \sqrt{3} then sec θ = ?

Foundation

Mathematics Foundation

Introduction to Trigonometry

Question

If $tanθ = \sqrt{3}$ then sec θ = ?

$\frac{1}{2}$

$\frac{\sqrt{3}}{2}$

$\frac{2}{\sqrt{3}}$

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Given tan θ = √3, we know from standard angles that θ = 60° (or π/3 radians).

Secant is the reciprocal of cosine. For θ = 60°, cos 60° = 1/2.

Therefore, sec θ = 1 / cos θ = 1 / (1/2) = 2.

Final answer: $2$