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Question
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin theta = 11/5`
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Solution
We know `sin theta = "opposite side"/"hypotenuse" = 11/15`
Consider right-angled Δle ACB
Let x = ๐๐๐๐๐๐๐๐ก ๐ ๐๐๐
By applying Pythagoras
๐ด๐ต2 = ๐ด๐ถ2 + ๐ต๐ถ2
225 = 121+๐ฅ2
๐ฅ2 = 225 -121
๐ฅ2 = 104
`x = sqrt104`
`cos = "adjacent side"/"hypotenuse" = sqrt(104/15)`
`tan = "opposite side"/"adjacent side" = 11/sqrt104`
`cosec theta = 1/sin theta = 15/11`
`sec = 1/cos theta = 15/sqrt104`
`cot = 1/ tan theta = sqrt104/11`
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