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

Mathematics
JAMB 2013

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. \(1\frac{2}{5}\)
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Correct Answer: Option D
Explanation

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

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

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

= 5

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

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

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

There is an explanation video available below.


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Explanation Video

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WAEC May/June 2024 - Practice for Objective & Theory - From 1988 till date, download app now - 99995
WAEC Past Questions, Objective & Theory, Study 100% offline, Download app now - 24709
Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts
WAEC offline past questions - with all answers and explanations in one app - Download for free
WAEC May/June 2024 - Practice for Objective & Theory - From 1988 till date, download app now - 99995
WAEC Past Questions, Objective & Theory, Study 100% offline, Download app now - 24709
Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts
WAEC offline past questions - with all answers and explanations in one app - Download for free