If tanθ = \frac{8}{15} then cosec θ = ?

Foundation

Mathematics Foundation

Introduction to Trigonometry

Question

If $tanθ = \frac{8}{15}$ then cosec θ = ?

$\frac{15}{17}$

$\frac{8}{17}$

$\frac{17}{8}$

$\frac{17}{15}$

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Given tanθ = 8/15, we can construct a right triangle where the opposite side is 8 and the adjacent side is 15. Using the Pythagorean theorem, the hypotenuse is:

$\sqrt{8^{2} + 15^{2}} = \sqrt{64 + 225} = \sqrt{289} = 17$

Cosecant (cosecθ) is the reciprocal of sine. Since sinθ = opposite/hypotenuse = 8/17, then cosecθ = hypotenuse/opposite = 17/8.

Final answer: $\frac{17}{8}$