JAMB - Mathematics (2010 - No. 42)
If cot\(\theta\) = \(\frac{8}{15}\), where \(\theta\) is acute, find sin\(\theta\)
\(\frac{8}{17}\)
\(\frac{15}{17}\)
\(\frac{16}{17}\)
\(\frac{13}{17}\)
Explicació
cot\(\theta\) = \(\frac{1}{\cos \theta}\)
= \(\frac{8}{15}\)(given)
tan\(\theta\) = \(\frac{15}{8}\)
By Pythagoras' theorem,
x\(^2\) = 15\(^2\) + 8\(^2\)
x\(^2\) = 225 + 64 = 289
x = \(\sqrt{289}\)
= 17
Hence sin\(\theta\) = \(\frac{15}{x}\)
= \(\frac{15}{17}\)
= \(\frac{8}{15}\)(given)
tan\(\theta\) = \(\frac{15}{8}\)
By Pythagoras' theorem,
x\(^2\) = 15\(^2\) + 8\(^2\)
x\(^2\) = 225 + 64 = 289
x = \(\sqrt{289}\)
= 17
Hence sin\(\theta\) = \(\frac{15}{x}\)
= \(\frac{15}{17}\)