If sin θ = \(\frac{4}{5}\) where 0° &ang; θ &ang; 90º, what is the value...

If sin θ = \(\frac{4}{5}\) where 0° ∠ θ ∠ 90º, what is the value of cos θ + tan θ?

A. \(\frac{14}{15}\)
B. \(\frac{29}{15}\)
C. \(\frac{13}{8}\)
D. \(\frac{144}{15}\)
E. \(\frac{24}{5}\)

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 = \(\frac{3}{5}\) + \(\frac{4}{3}\) = \(\frac{29}{15}\)

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