Question

If 2 cos θ = `sqrt(3)`, then find all the trigonometric ratios of angle θ

Answer 1

2 cos θ = `sqrt(3)`

⇒ cos θ = `sqrt(3)/2`

AB² = AC² – BC² 

= `2^2 - (sqrt(3))^2`

⇒ 4 – 3 = 1

AB = `sqrt(1)` = 1

sin θ = `"opposite side"/"hypotenuse" = 1/2`

cos θ = `"adjacent side"/"hypotenuse" = sqrt(3)/2`

tan θ = `"opposite side"/"adjacent side" = 1/sqrt(3)`

cosec θ = `"hypotenuse"/"opposite side"` = 2

sec θ = `"hypotenuse"/"adjacent side" = 2/sqrt(3)`

cot θ = `"adjacent side"/"opposite side" = sqrt(3)`