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Question
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`cot theta = 12/5`
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Solution
`cot alpha = "๐๐๐๐๐๐๐๐ก ๐ ๐๐๐"/"๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐" = 12/5`
Now consider a right-angled Δle ABC,
By applying Pythagoras theorem
๐ด๐ถ2 = ๐ด๐ต2 + ๐ต๐ถ2
๐ฅ2 = 25 + 144
`x^2 = 169 = sqrt169`
๐ฅ = 13
`tan theta = 1/cot theta = (1/12)/5 = 5/12`
`sin theta = "๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐"/"โ๐ฆ๐๐๐ก๐๐๐ข๐ ๐" = 5/13`
`cos theta = "๐๐๐๐๐๐๐๐ก ๐ ๐๐๐"/"โ๐ฆ๐๐๐ก๐๐๐ข๐ ๐" = 12/13`
`cosec theta = 1/sin theta = 1/(5/13) = 13/5`
`sec theta = 1/cos theta = 1/(12/13) = 13/12`
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