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Trigonometric Identities

If cos θ=4/5,...

Question

If $c o s θ = \frac{4}{5}$ , find all other trigonometric ratios of angle $θ$

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Solution

$g i v e n space space space cos theta equals 4 over 5 sin squared theta plus cos squared theta equals 1 sin squared theta plus left parenthesis 16 over 25 right parenthesis equals 1 sin squared theta equals 1 minus 16 over 25 sin squared theta equals 9 over 25 sin theta equals 3 over 5 tan theta equals fraction numerator sin theta over denominator cos theta end fraction equals fraction numerator begin display style 3 over 5 end style over denominator begin display style 4 over 5 end style end fraction equals 3 over 4 cos e c theta equals fraction numerator 1 over denominator sin theta end fraction equals 5 over 3 s e c theta equals fraction numerator 1 over denominator cos theta end fraction equals 5 over 4 c o t theta equals fraction numerator 1 over denominator tan theta end fraction equals 4 over 3$

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