If \(\tan \theta = \frac{3}{4}\), find the value of \(\sin \theta + \cos \theta\).
A
\(1\frac{1}{3}\)
B
\(1\frac{2}{3}\)
C
\(1\frac{3}{5}\)
D
\(1\frac{2}{5}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\tan \theta = \frac{opp}{adj} = \frac{3}{4}\)
\(hyp^{2} = opp^{2} + adj^{2}\)
\(hyp = \sqrt{3^{2} + 4^{2}}\)
= 5
\(\sin \theta = \frac{3}{5}; \cos \theta = \frac{4}{5}\)
\(\sin \theta + \cos \theta = \frac{3}{5} + \frac{4}{5}\)
= \(\frac{7}{5} = 1\frac{2}{5}\)
Source: Myschool Past Questions Archive (Record #54925)