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Question
In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.
`sin theta = sqrt3/2`
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Solution
`sin theta = sqrt3/2`
We know `sin theta = "opposide side"/"Hyotence" = sqrt3/2`
Now consider right-angled Δle ABC
Let x = adjacent sidead
By applying Pythagoras
𝐴𝐵2 = 𝐴𝐶2 + 𝐵𝐶2
4 = 3+𝑥2
𝑥2 = 4 − 3
𝑥2 = 1
𝑥 = 1
`cos = "opposite side"/"Hypotenuse" = 1/2`
`tan = "Oppsite side"/"hypotenuse" = sqrt3/1 = sqrt3`
`cosec theta = 1/sin theta = 1/(sqrt3/2) = 2/sqrt3`
sec = `1/cos theta = (1/1)/2 = 2`
`cot = 1/tan theta = 1/sqrt3`
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