1 Answer

Sansalk · Answer 1 · 2023-07-19T18:59:32+0000

Answer:

x = 30 degrees

x = 60 degrees

Step-by-step explanation:

Given the below trig function;

$\sin 2x=\frac{\sqrt[]{3}}{2}$

To solve for x, let's take the inverse sine of both sides of the equation, we'll have;

$\begin{gathered} 2x=\sin ^(-1)(\sqrt[]{(3)/(2))} \\ 2x=60 \\ x=(60)/(2) \\ x=30^(\circ) \end{gathered}$

To find the 2nd solution, we know that, in the 1st and 2nd quadrants, the sine function is always positive. So we'll have;

$\begin{gathered} 2x=(180-60) \\ 2x=120 \\ x=(120)/(2) \\ x=60^(\circ) \end{gathered}$

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