If sinθ = - \(\frac{3}{5}\) andθ lies in the third quadrant, find cosθ
A. \(\frac{4}{5}\)
B. - \(\frac{5}{4}\)
C. \(\frac{5}{4}\)
D. - \(\frac{4}{5}\)
Correct Answer: D
Explanation
Where sinθ = \(\frac{opp}{hyp}\)→\(\frac{-3}{5}\)
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
cosθ =\(\frac{adj}{hyp}\)→\(\frac{4}{5}\)
In third quadrant:cosθ is negative→ - \(\frac{4}{5}\)
There is an explanation video available below.
