If sin - frac 3 5 and lies in the third quadran... - JAMB Mathematics 2022 Question

sin θ = \(\frac{opp}{hyp}\) → \(\frac{-3}{5}\)

opp = -3, hyp = 5

using Pythagoras' formula:

hyp\(^2\) = adj\(^2\) + opp\(^2\)

adj\(^2\) = hyp\(^2\) - opp\(^2\)

adj\(^2\) = 5\(^2\) - 3\(^2\) → 25 - 9

adj\(^2\) = 16

adj = 4

cos θ = \(\frac{adj}{hyp}\) → \(\frac{4}{5}\)

In the third quadrant, cos θ is negative

=> - \(\frac{4}{5}\)