If sin \theta = \(\frac{4}{5}\) where 0^\circ ∠ \theta ∠ 90º, what is the value of cos \theta + tan \theta?
A
\(\frac{14}{15}\)
B
\(\frac{29}{15}\)
C
\(\frac{13}{8}\)
D
\(\frac{144}{15}\)
E
\(\frac{24}{5}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
0^\circ ∠ \theta ∠ 90º,
From the diagram above, the adjacent by Pythagoras theorem = 3
Cos \theta = \(\frac{\text{adj}}{\text{hyp}}\) = \(\frac{3}{5}\)
Tan \theta = \(\frac{\text{opp}}{\text{adj}}\) = \(\frac{4}{3}\)
cos \theta + tan \theta = \(\frac{3}{5}\) + \(\frac{4}{3}\) = \(\frac{29}{15}\)
Source: Myschool Past Questions Archive (Record #41960)