If \(\sin\theta = \frac{3}{5}, 0° < \theta < 90°\), evaluate \(\cos(180 - \theta)\).
FURTHER MATHEMATICS
WAEC 2018
If \(\sin\theta = \frac{3}{5}, 0° < \theta < 90°\), evaluate \(\cos(180 - \theta)\).
- A. \(\frac{4}{5}\)
- B. \(\frac{3}{5}\)
- C. \(\frac{-3}{5}\)
- D. \(\frac{-4}{5}\)
Correct Answer: D. \(\frac{-4}{5}\)
Explanation
Given \(\sin \theta = \frac{3}{5} \implies opp = 3, hyp = 5\)
Using Pythagoras' Theorem, we have \( adj = \sqrt{5^{2} - 3^{2}} = \sqrt{16} = 4\)
\(\therefore \cos \theta = \frac{4}{5}, 0° < \theta < 90°\)
In the quadrant where \(180° - \theta\) lies is the 2nd quadrant and here, only \(\sin \theta = +ve\).
\(\therefore \cos (180 - \theta) = -ve = \frac{-4}{5}\)
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