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

Question

asked Mar 6, 2023 44.9k views

1 Answer

Quinnj · Answer 1 · 2023-03-12T19:53:23+0000

Answer:

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:

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

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