Question

If cot θ = 2, find the values of all T-ratios of θ.

Answer 1

Let us first draw a right ΔABC, right angled at B and ∠𝐶 = 𝜃
Now, we know that cot θ = `"𝐵𝑎𝑠𝑒"/" 𝑃𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟" = (BC)/(AB) = 2`

So, if BC = 2k, then AB = k, is a positive number.
Now, using Pythagoras theorem, we have:
`AC^2 = AB^2 + BC^2 = (2K)^2 + (K)^2`
`⟹ AC^2 = 4K^2 + K^2 = 5K^2`
`⟹ AC= sqrt(5k)`
Now, finding the other T-ratios using their definitions, we get:

Sin θ = `(AB)/(AC) = 5/(sqrt(5k)) = 1/(sqrt (2)`

∴ Cos θ = `1/ (cot θ ) = 1/2 , cosec θ = 1/(sin θ ) = sqrt(5) and secθ = 1/ (cos θ) = sqrt(5)/2`