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