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Question

If cos θ=45, 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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