Question

16Select the correct answer from each drop-dowrormenu.Complete the statement.The solutions of sin2x = sareand.ResetNext

Answer 1

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}`