Question

Find all solutions to the equation. 2sin theta - squareroot 3 = 0

Answer 1

Answer:

$\theta$ =2mπ + π/3 for m ∈ Z.

Step-by-step explanation:

Given the equation $2sin\theta - \sqrt{3} = 0$, we are to find all the values of $\theta$ that satisfies the equation.

$2sin\theta - \sqrt{3} = 0\\\\2sin\theta = \sqrt{3} \\\\sin\theta = \sqrt{3}/2 \\\\\theta = sin{-1} \sqrt{3}/2 \\\\\theta = 60^0$

General solution for sin$\theta$ is $\theta$ = nπ + (-1)ⁿ ∝, where n ∈ Z.

If n is an even number say 2m, then $\theta$ = (2m)π + ∝ where ∝ = 60° = π/3

Hence, the general solution to the equation will be $\theta$ = 2mπ + π/3 for m ∈ Z.