Question

if cot theta= √3, then find the value of theta.
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Answer 1

Answer:

Theta is equal to 30 degree

Step-by-step explanation:

BECAUSE the value of root 3 has cot theta on 30 degree

Answer 2

θ = (π/6), (7π/6) are the principal solutions and θ = nπ + (π/6) is the general solution of the equation.

Given:

cotθ = √3

To find:

The value of 'θ'.

Solution:

                        cotθ = √3

Let's find the principal solution to the above equation:

→ As we know cot (π/6) = √3

                      ∴ θ = π/6

→ For the cot function we know that: cot (π + A) = cotA

             ∴ θ = π + (π/6) = 7π/6

→ Hence the principal solutions are: θ = (π/6), (7π/6)

→ Now let's find the general solution for the above equation:

As we know that cot functions repeat itself after an interval of π:

                ∴ θ = nπ + (π/6) where 'n'∈Integers (Z)

→ θ = nπ + (π/6) would be the general solution of the equation: cotθ = √3

Therefore θ = (π/6), (7π/6) are the principal solutions of the equation and θ = nπ + (π/6) is the general solution of the equation.

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