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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 alpha = 5/12`
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Solution
`tan alpha = 5/12`
We know that `tan alpha ="opposite side/adjacent side"= 5/12`
Now consider a right-angled Δle ABC
Let x = hypotenuse .By applying Pythagoras theorem
𝐴𝐶2 = 𝐴𝐵2 + 𝐵𝐶2
𝑥2 = 52 + 122
𝑥2 = 25 + 144 = 169
𝑥 = 13
`sin α = "adjacent side"/"hypotenuse"= 5/13`
`cos α = "adjacent side"/"hypotenuse" = 12/13`
cot α = `1/tan alpha = 12/15``
cosec α = `1/sin alpha = (1/5)/13 = 13/5`
sec α = `1/cos alpha = (1/12)/13 = 13/12`
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