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Question
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cosec theta = sqrt10`
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Solution
consider a right-angled Δle ABC, we get
Let x be the adjacent side.
By applying Pythagoras theorem
𝐴𝐶2 = 𝐴𝐵2 + 𝐵𝐶2
`(sqrt10)^2 = 1^2 + x^2`
x2 = 10 − 1 = 9
x = 3
`sin theta = 1/cosec theta = 1/sqrt10`
`cos theta = "adjacent"/"hypotenuse" = 3/sqrt10`
`tan theta = "opposite sides"/"adjacebt side" = 1/3`
`sec theta = 1/cos theta = sqrt10/3`
`cot theta = 1/tan theta = (1/1)/3 = 3`
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