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Question
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`cos theta = 7/25`
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Solution
We know that `cos theta = "adjacent side"/"hypotence"`
Now consider a right-angled Δle ABC
Let x be the opposite side.
By applying Pythagoras theorem
𝐴𝐶2 = 𝐴𝐵2 + 𝐵𝐶2
(25)2 = 𝑥2 + 72
625 - 49 = 𝑥2
`576 = sqrt576 = 24`
`sin theta = "opposite side"/"hypotenuse"= 24/25`
`tan theta = "opposite side"/"adjacent side" = 24/7`
`cosec theta = 1/sin theta = (1/3)/5 = 25/24`
`sec theta = 1/cos theta = (1/4)/5 = 25/7`
`cot theta = 1/tan theta = (1/3)/4 = 7/24`
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