If sin θ = \(\frac{4}{5}\) where 0° ∠ θ ∠ 90º, what is the value of cos θ + tan θ?
- \(\frac{14}{15}\)
-
\(\frac{29}{15}\)
- \(\frac{13}{8}\)
- \(\frac{144}{15}\)
- \(\frac{24}{5}\)
The correct answer is: B
Explanation
0° ∠ θ ∠ 90º,
From the diagram above, the adjacent by Pythagoras theorem = 3
Cos θ = \(\frac{\text{adj}}{\text{hyp}}\) = \(\frac{3}{5}\)
Tan θ = \(\frac{\text{opp}}{\text{adj}}\) = \(\frac{4}{3}\)
cos θ + tan θ = \(\frac{3}{5}\) + \(\frac{4}{3}\) = \(\frac{29}{15}\)