Question

Given sec θ = $\sf{\frac{13}{12}}$.Calculate all other trigonometric ratios.​

Answer 1

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Answer 2

Answer:

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It is given that:

sec θ = hypotenuse / side adjacent to ∠θ = AC/AB = 13/12

Let AC = 13k and AB = 12k, where k is a positive integer.

Applying Pythagoras theorem in Δ ABC, we obtain:

AC2 = AB2 + BC2

BC2 = AC2 - AB2

BC2 = (13k)2 - (12k)2

BC2 = 169 k2 - 144 k2

BC2 = 25k2

BC = 5k

sin θ = side opposite to ∠θ / hypotenuse = BC/AC = 5/13

cos θ = side adjacent to ∠θ / hypotenuse = AB/AC = 12/13

tan θ = side opposite to ∠θ / side adjacent to ∠θ = BC/AB = 5/12

cot θ = side adjacent to ∠θ / side opposite to ∠θ = AB/BC = 12/5

cosec θ = hypotenuse / side opposite to ∠θ = AC/BC = 13/5