Question

How do you find the value of `cot (-150)`?

Answer 1

Cot (-150) = `sqrt(3)`

Explanation:

Cot(-150) = Cos(-150) / Sin(-150)
Now Cos (-x) = Cos (x) and Sin (-x) = -Sin (x)
Hence Cot(-150) = Cos (150) /(-sin(150))
= Cos(180 - 30) / (-Sin (180 - 30))
Also Cos (180 - x) = -Cos(x) and Sin (180 - x) = Sin (x)
So the expression becomes
-Cos (30) / (-Sin(30)
= Cos (30) / Sin (30)
Now Cos (30) = `sqrt (3) / 2` and Sin (30) = `1/2`
Hence Cos(30) / Sin(30) = `sqrt (3) / 2 / 1 /2`
= `sqrt(3) / 2 * 2 = sqrt(3)`