Calculate all the values of $x$ between $0$ and $2\pi$, without using calculator. $2\sin 2x=\sqrt2$
thanks.
Calculate all the values of $x$ between $0$ and $2\pi$, without using calculator. $2\sin 2x=\sqrt2$
thanks.
Okay, now you have $\sin 2x=\frac1{\sqrt2}$. You should know an angle $\theta$ such that $0\le\theta<\pi/2$ and $\sin\theta=\frac1{\sqrt2}$; if it doesn't immediately occur to you, think of the right triangles whose angles you know. There's only one other angle between $0$ and $2\pi$ whose sine is $\frac1{\sqrt2}$; what is it? (It helps here to be familiar with the circle approach to sines and cosines, but you can also get it by considering the graph of $y=\sin x$.)
${}{}{}{}{}\varnothing {}{}{}{}$ Oh come on!
The solution to the revised question comes from finding angles with a since ratio of $\dfrac{\sqrt2}{2} = \dfrac{1}{\sqrt2}$. Write out two periods of such solutions (why?) and then divide the angles by two.