JAMB - Mathematics (2022 - No. 6)

If sin θ = - \(\frac{3}{5}\) and θ lies in the third quadrant, find cos θ

\(\frac{4}{5}\)

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

\(\frac{5}{4}\)

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

Where 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 third quadrant: cos θ is negative → - \(\frac{4}{5}\)