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jmartinez638
 one year ago
How do you find all the solutions for 'sin(x/2  pi/4) = sqrt2/2'?
jmartinez638
 one year ago
How do you find all the solutions for 'sin(x/2  pi/4) = sqrt2/2'?

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phi
 one year ago
Best ResponseYou've already chosen the best response.1solutions imply an equation equations have an = sign your expression does not. is that a typo?

jmartinez638
 one year ago
Best ResponseYou've already chosen the best response.1Yes, So sorry = sqrt2/2

phi
 one year ago
Best ResponseYou've already chosen the best response.1do you know how to "undo" sin ?

jmartinez638
 one year ago
Best ResponseYou've already chosen the best response.1Like using identities?

phi
 one year ago
Best ResponseYou've already chosen the best response.1more like, do \(\sin^{1} \) to both sides

phi
 one year ago
Best ResponseYou've already chosen the best response.1\[ \sin^{1} \left(\sin\left(\frac{x}{2}  \frac{\pi}{4}\right) \right)=\sin^{1} \frac{\sqrt2}{2} \]

phi
 one year ago
Best ResponseYou've already chosen the best response.1on 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
 one year ago
Best ResponseYou've already chosen the best response.1on 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
 one year ago
Best ResponseYou've already chosen the best response.145 degrees or \[\pi\]/4

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes. but because the question asks for *all* solutions we should eyeball the graph for sin dw:1440367395779:dw

phi
 one year ago
Best ResponseYou've already chosen the best response.1so one family of solutions is pi/4 + 2pi n and the other is 3pi/4 + 2pi n where n is any integer

jmartinez638
 one year ago
Best ResponseYou've already chosen the best response.1Oh that makes sense. In relation to the graph especially...

phi
 one year ago
Best ResponseYou've already chosen the best response.1so we should try to solve \[ \frac{x}{2}  \frac{\pi}{4}=\frac{\pi}{4} + 2\pi n\] and also \[ \frac{x}{2}  \frac{\pi}{4}=\frac{3\pi}{4} + 2\pi n\]

jmartinez638
 one year ago
Best ResponseYou've already chosen the best response.1\[(8n+5)\pi \div2\] for the first one

jmartinez638
 one year ago
Best ResponseYou've already chosen the best response.1Is that a viable answer?

phi
 one year ago
Best ResponseYou've already chosen the best response.1\[ \frac{x}{2}  \frac{\pi}{4}=\frac{\pi}{4} + 2\pi n \\ \frac{x}{2} = \frac{\pi}{2} + 2\pi n \\ x= \pi + 4 \pi n \]

jmartinez638
 one year ago
Best ResponseYou've already chosen the best response.1Oops yeah, I must've looked at the second one and not the first :3 Let me try the first...

jmartinez638
 one year ago
Best ResponseYou've already chosen the best response.1I got x=(4n+1)*pi

jmartinez638
 one year ago
Best ResponseYou've already chosen the best response.1Does (8n+5)π÷2 work?

jmartinez638
 one year ago
Best ResponseYou've already chosen the best response.1Ah, I seem to have made a mistake. How about \[x=2(2n+1)\pi\]?

phi
 one year ago
Best ResponseYou've already chosen the best response.1yes, that looks good. though people would probably write it as 2pi(2n+1)

phi
 one year ago
Best ResponseYou've already chosen the best response.1and of course we have to say n is any integer

jmartinez638
 one year ago
Best ResponseYou've already chosen the best response.1Ok, of course. So those two equations, with 'n' designated as any integer, would be the solutions to that equation?

jmartinez638
 one year ago
Best ResponseYou've already chosen the best response.1That makes a lot of sense, thank you so much!
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