Question

If `sin θ = 1/2` then cot θ = ?

Options

• `sqrt(3)/2`

• 1

• `sqrt(3)`

• `1/sqrt(3)`

Answer 1

`bb(sqrt(3))`

Explanation:

`sin θ = 1/2`

⇒ `(BC)/(AC) = 1/2`

Let BC = k. Then, AC = 2k.

AB² = (AC² – BC²)

= (4k² – k²) 

= 3k²

∴ `AB = sqrt(3)k`.

∴ `cot θ = (AB)/(BC)`

= `(sqrt(3)k)/k`

= `sqrt(3)`