Question

2sin(x-(pi/6)-sqrt2

Answer 1

what is it you need to do?

Answer 2

2sin(x-(pi/6))-sqrt2=0

Answer 3

help me solve it

Answer 4

can you 'isolate' the x term and move all the constants to the same side as the equal sign

Answer 5

i have no idea how i start solving it, can u help?

Answer 6

\(\bf 2sin\left(x-\cfrac{\pi}{6}\right)-\sqrt{2}=0\implies 2sin\left(x-\cfrac{\pi}{6}\right)=\sqrt{2}\\ \quad \\\implies sin\left(x-\cfrac{\pi}{6}\right)=\cfrac{\sqrt{2}}{2}\\ \quad \\
\textit{taking }sin^{-1}\textit{ to both sides}\\ \quad \\
sin^{-1}\left[sin\left(x-\cfrac{\pi}{6}\right)\right]=sin^{-1}\left[\cfrac{\sqrt{2}}{2}\right]\\ \quad \\
\textit{recall that }\qquad sin^{-1}(sin(\theta))=\theta\qquad thus\\ \quad \\
sin^{-1}\left[sin\left(x-\cfrac{\pi}{6}\right)\right]=sin^{-1}\left[\cfrac{\sqrt{2}}{2}\right]\implies x-\cfrac{\pi}{6}=sin^{-1}\left[\cfrac{\sqrt{2}}{2}\right]
\)

Answer 7

yea,
i'll start you, but you need to finish ^_^
if I do this, what does the equation look like now?