If \(\tan \theta = \frac{3}{4}\), find the value of \(\sin \theta + \cos \theta\).

Explanation

\(\tan \theta = \frac{opp}{adj} = \frac{3}{4}\)

\(hyp^{2} = opp^{2} + adj^{2}\)

\(hyp = \sqrt{3^{2} + 4^{2}}\)

= 5

\(\sin \theta = \frac{3}{5}; \cos \theta = \frac{4}{5}\)

\(\sin \theta + \cos \theta = \frac{3}{5} + \frac{4}{5}\)

= \(\frac{7}{5} = 1\frac{2}{5}\)

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