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If cot\(\theta\) = \(\frac{8}{15}\), where \(\theta\) is acute, find sin\(\theta\)

Mathematics
JAMB 2010

If cot\(\theta\) = \(\frac{8}{15}\), where \(\theta\) is acute, find sin\(\theta\)

  • A. \(\frac{8}{17}\)
  • B. \(\frac{15}{17}\)
  • C. \(\frac{16}{17}\)
  • D. \(\frac{13}{17}\)
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Correct Answer: Option B
Explanation

cot\(\theta\) = \(\frac{1}{\cos \theta}\)

= \(\frac{8}{15}\)(given)

tan\(\theta\) = \(\frac{15}{18}\)

By Pythagoras theorem,

x2 = 152 + 82

x2 = 225 + 64 = 289

x = \(\sqrt{289}\)

= 17

Hence sin\(\theta\) = \(\frac{15}{x}\)

= \(\frac{15}{17}\)

There is an explanation video available below.


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Explanation Video

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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
WAEC Past Questions, Objective & Theory, Study 100% offline, Download app now - 24709
WAEC May/June 2024 - Practice for Objective & Theory - From 1988 till date, download app now - 99995
WAEC offline past questions - with all answers and explanations in one app - Download for free