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In the Following, One of the Six Trigonometric Ratios is Given. Find the Values of the Other Trigonometric Ratios. `Tan Alpha = 5/12` - CBSE Class 10 - Mathematics

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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`

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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Solution In the Following, One of the Six Trigonometric Ratios is Given. Find the Values of the Other Trigonometric Ratios. `Tan Alpha = 5/12` Concept: Trigonometric Ratios.
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