Question

if cos theta =5/13 then find: (a) sin theta (b) tan theta (c) sec theta



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Answer 1

here you go. I have given the answer

Answer 2

$here \: \cos \theta = \frac{5}{13} \\ \\ we \: knows \: that.. \\ \: \sin\theta = \sqrt{1 - { \cos }^{2} \theta } \\ \\ \therefore \sin\theta = \sqrt{1 - {( \frac{5}{13}) }^{2} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{1 - \frac{25}{169} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{ \frac{169 - 25}{169} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{ \frac{144}{169} } \\ \therefore \sin\theta = \frac{12}{13} \\ \\ now..... \\ \\ \tan \theta = \frac{ \sin\theta }{ \cos\theta } \\ \\ \therefore \tan\theta \: = \frac{ \frac{12}{13} }{ \frac{5}{13} } \\ \\ \therefore \: \tan \theta \: = \frac{12}{5} \\ \\ now.... \\ \sec\theta \: = \frac{1}{ \cos\theta } \\ \\ \therefore \: \sec\theta \: = \frac{1}{ \frac{5}{13} } \\ \\ \therefore \: \sec \theta = \frac{13}{5}$
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