How do you find all the solutions for 'sin(x/2 - pi/4) = sqrt2/2'?

Question

phi · Answer

solutions imply an equation
equations have an = sign
your expression does not. is that a typo?

jmartinez638 · Answer

Yes, So sorry = sqrt2/2

jmartinez638 · Answer

Edited original.

phi · Answer

do you know how to "undo"  sin ?

jmartinez638 · Answer

Like using identities?

phi · Answer

more like, do  $\sin^{-1} $ to both sides

phi · Answer

$$ \sin^{-1} \left(\sin\left(\frac{x}{2} - \frac{\pi}{4}\right) \right)=\sin^{-1} \frac{\sqrt2}{2} $$

phi · Answer

on the left side, the inverse sin of the sin  undoes the sin
we are left with
$$ \frac{x}{2} - \frac{\pi}{4}=\sin^{-1} \frac{\sqrt2}{2} $$

phi · Answer

on the right side it is asking for an angle
what angle is it where sin of that angle = sqr(2)/2
we want it in radians
and it is an angle people memorize  (so you should too)

jmartinez638 · Answer

45 degrees or $$\pi$$/4

phi · Answer

yes.  but because the question asks for *all* solutions
we should eyeball the graph for sin
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