if tanθ = \(frac{3}{4}\), 180° < θ < 270°, find the value of cosθ.
A
\(\frac{4}{5}\)
B
\(\frac{3}{5}\)
C
-\(\frac{4}{5}\)
D
-\(\frac{3}{5}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
tan\theta = \(frac{3}{4}\) → tan\theta = 0.75
\theta = tan\(^{-1}\)[0.75] → 36.8698^\circ
cos\theta = cos[36.8698^\circ]
→ 0.800 or \(frac{4}{5}\)
However; in the third quadrant Cosine is negative
i.e -\(frac{4}{5}\)
Source: WAEC / JAMB / NECO Classroom Archive (Record #61240)