Question

If cosθ = $\frac{4}{5}$, then tanθ = ?
(a) $\frac{3}{4}$
(b) $\frac{4}{3}$
(c) $\frac{3}{5}$
(d) $\frac{5}{3}$

Answer 1

(a) $\frac{3}{4}$
Since cosθ = $\frac{4}{5}$ but cosθ = $\frac{AB}{AC}$
So, $\frac{AB}{AC}$ = $\frac{4}{5}$
Thus, AB = 4k and AC = 5k


Using Pythagoras theorem in triangle ABC, we have:
AC² = AB² + BC²
⇒ BC² = AC² $-$ AB²
⇒ BC² = (5k)² $-$ (4k)²
⇒ BC² = 9k²
⇒ BC = 3k
∴ tanθ = $\frac{BC}{AB}$ = $\frac{3}{4}$