Question

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

Write your answer in radians in terms of pi, and use the "or" button as necessary.
Example: theta = pi/5 + 2 k pi, k element Z or theta = pi/7 + k pi, k element Z

Answer 1

`\theta` =2mπ + π/3 for m ∈ Z.

Explanation:

Given the equation
`2sin\theta - √(3) = 0`, we are to find all the values of
`\theta` that satisfies the equation.

`2sin\theta - √(3) = 0\\\\2sin\theta = √(3) \\\\sin\theta = √(3)/2 \\\\\theta = sin{-1} √(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.