Question

EXERCIS
5
1. Given that tan =5/2
and angle O is an acute angle,

find sin 0 and cos O.
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Answer 1

Answer:

$tanx = \frac{5}{2} \\ we \: know \\ {sec}^{2} x - {tan}^{2} x = 1 \\ {sec}^{2} x - {( \frac{5}{2} )}^{2} = 1 \\ = 1 + \frac{25}{4} \\ = \frac{29 }{4} \\ secx \: = \frac{ \sqrt{29} }{2} \\ = > cosx = \frac{2}{ \sqrt{29} } \\ now \: {sin}^{2} x + {cos}^{2} x = 1 \\ {sin}^{2} x + \frac{4}{29} = 1 \\ = 1 - \frac{4}{29} \\ = \frac{25}{29} \\ therefore \: sinx \: = \frac{5}{ \sqrt{29} }$