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Question
In the following, one of the six trigonometric ratios is given. Find the values of the other trigonometric ratios.
`tan theta = 8/15`
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Solution
We know that `tan theta = "๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐"/"๐๐๐๐๐๐๐๐ก ๐ ๐๐๐" = 8/15`
Now consider a right-angled Δle ABC.
By applying Pythagoras theorem
๐ด๐ถ2 = ๐ด๐ต2 + ๐ต๐ถ2
๐ฅ2 = 82 + 152
๐ฅ2 = 225 + 64 = 289
`x = sqrt289 = 17`
`sin theta = "๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐"/"โ๐ฆ๐๐๐ก๐๐๐ข๐ ๐" = 8/17`
`cos theta = "๐๐๐๐๐๐๐๐ก ๐ ๐๐๐"/"โ๐ฆ๐๐๐ก๐๐๐ข๐ ๐" = 15/17`
`tan theta = "๐๐๐๐๐ ๐๐ก๐ ๐ ๐๐๐"/"๐๐๐๐๐๐๐๐ก ๐ ๐๐๐" = 8/15`
`cot theta = 1/tan theta = 1/(8/15) = 15/8`
`cosec theta = 1/sin theta = (1/8)/17 = 17/8`
`sec theta = 1/cos theta= (1/15)/17 = 17/15`
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