Question

solve the equation on the interval (0,2pie) for sin4theta =squareroot 3/2

Answer 1

Assuming the equation is:\[\sin 4\theta=\frac{ \sqrt{3} }{ 2 }\]It is known that
\[\sin \frac{ \pi }{ 3 }=\frac{ \sqrt{3} }{ 2 }\]SO now you can write this equation in the standard form:\[\sin 4\theta=\sin \frac{ \pi }{ 3 }\]
The standard form of the equation has this solutions:\[\sin a=\sin b \rightarrow a=b, or, a=\pi-b\]Normally there are infinitely more solutions: all multiples of 2pi added.
In this case you have only 2 solutions, because you only have to look in the interval [0, 2pi].
Now try to use this general solution in this case.

Answer 2

Thank you so much , now i see my error

Answer 3

You are welcome!