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

Answer:

60°, 120°, and 420°.

Explanation:

Given:

$\sin\theta=\frac{\sqrt{3}}{2}$

Take the arcsin of both sides:

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

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

$\begin{gathered} \theta=60\degree \\ \theta=120\operatorname{\degree} \\ \theta=60\operatorname{\degree}+360\degree=420\degree \end{gathered}$

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