Question

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

`sin theta = sqrt3/2`

Answer 1

`sin theta = sqrt3/2`

We know `sin theta = "opposide side"/"Hyotence" = sqrt3/2`

Now consider right-angled Δ^le 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`