If cot theta frac 8 15 where theta is acute fin... - JAMB Mathematics 2010 Question
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
\(\frac{13}{17}\)
correct option: b
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\(\theta\) = \(\frac{15}{x}\)
= \(\frac{15}{17}\)
= \(\frac{8}{15}\)(given)
tan\(\theta\) = \(\frac{15}{18}\)
By Pythagoras theorem,
x2 = 152 + 82
x2 = 225 + 64 = 289
x = \(\sqrt{289}\)
= 17
Hence sin\(\theta\) = \(\frac{15}{x}\)
= \(\frac{15}{17}\)
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