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In the Following, Trigonometric Ratios Are Given. Find the Values of the Other Trigonometric Ratios. `Sin Theta = Sqrt3/2` - Mathematics

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Question

In the following, trigonometric ratios are given. Find the values of the other trigonometric ratios.

`sin theta = sqrt3/2`

Sum
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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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Chapter 10: Trigonometric Ratios - Exercise 10.1 [Page 23]

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RD Sharma Mathematics [English] Class 10
Chapter 10 Trigonometric Ratios
Exercise 10.1 | Q 1.06 | Page 23

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