Question

Given sine of theta equals square root of three/ two determine three possible angles for theta on the domain of [0, infinity)

Answer 1

60°, 120°, and 420°.

Explanation:

Given:

`\sin\theta=(√(3))/(2)`

Take the arcsin of both sides:

`\begin{gathered} \theta=\arcsin((√(3))/(2)) \\ \theta=60\degree+360(n)\text{ or }\theta=120\degree+360(n),\theta\in[0,\infty) \end{gathered}`

Therefore, three possible angles for θ on the domain of [0, ∞) are:

Three possible angles are 60°, 120°, and 420°.