How do you find all six trigonometric function of #theta# if the point #(m, n)# is on the terminal side of #theta#?

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How do you find all six trigonometric function of #theta# if the point #(m, n)# is on the terminal side of #theta#?

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Answer 1 · 2017-03-18T05:09:23

#tan t = n/m#
#cos^2 t = 1/(1 + tan^2 t) = 1/(1 + n^2/(m^2)) = m^2/(m^2 + n^2)#
#cos t = +- m/(sqrt(m^2 + n^2))#
#sin^2 t = 1/(1 + cot^2 t) = 1/(1 + m/n) = n^2/(m^2 + n^2)#
#sin t = +- n/(sqrt(m^2 + n^2)#
#tan t = n/m#
#cot t = m/n#
#sec t = +- (sqrt(m^2 + n^2))/m#
#csc t = +- (sqrt(m^2 + n^2))/n#

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How do you find all six trigonometric function of #theta# if the point #(m, n)# is on the terminal side of #theta#?

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