General

[quote=Harri]Those tags =.=[/quote]

Lol the main reason I don't like to use tinypic in basil is that someone usually reviles asians trough the tags haha...

[quote=FaTaLP3NGU1N]sin(x)=±1/(√2)
sin(x)=1/(√2) or -1/(√2)

x=arcsin(1/(√2))=π/4+2πk or (π-π/4)+2πk

x=arcsin(-1/(√2))=-π/4+2πk or (π-(-π/4))+2πk[/quote]

Oh never mind I get it. I was just confused as how the inverse sine of 1/(√2) is π/4. I'm so used to it being root 2 over 2 lol.

[quote=Mathematician]I know how you got it I just don't get how you get from that to x=Ï€/4[/quote]

sin(x)=±1/(√2)
sin(x)=1/(√2) or -1/(√2)

x=arcsin(1/(√2))=π/4+2πk or (π-π/4)+2πk
since 0≤x<2π, x=π/4, 3π/4

x=arcsin(-1/(√2))=-π/4+2πk or (π-(-π/4))+2πk
since 0≤x<2π, x=7π/4, 5π/4

[quote=FaTaLP3NGU1N](2sin²(x)-1)=0
2sin²(x)=1
sin²(x)=1/2
sin(x)=±1/(√2)[/quote]

I know how you got it I just don't get how you get from that to x=Ï€/4

[quote=Mathematician]How did you get the "x=π/4" part? I get the others but the sin(x)=±1/(√2) part is what confuses me[/quote]

(2sin²(x)-1)=0
2sin²(x)=1
sin²(x)=1/2
sin(x)=±1/(√2)

[quote=FaTaLP3NGU1N]4sin³(x)+2sin²(x)-2sin(x)-1=0
(2sin²(x))(2sin(x)+1)-(2sin(x)+1)=0
(2sin²(x)-1)(2sin(x)+1)=0

2sin²(x)=1
sin(x)=±1/(√2)

x=Ï€/4
x=Ï€-(Ï€/4)=3Ï€/4
x=-Ï€/4=-Ï€/4+2Ï€=7Ï€/4
x=Ï€-(-Ï€/4)=5Ï€/4

2sin(x)+1=0
sin(x)=-1/2
x=-Ï€/6=-Ï€/6+2Ï€=11Ï€/6
x=Ï€-(-Ï€/6)=Ï€+Ï€/6=7Ï€/6

x=Ï€/4, 3Ï€/4, 7Ï€/4, 5Ï€/4, 11/6, 7Ï€/6[/quote]

How did you get the "x=π/4" part? I get the others but the sin(x)=±1/(√2) part is what confuses me

4sin³(x)+2sin²(x)-2sin(x)-1=0
(2sin²(x))(2sin(x)+1)-(2sin(x)+1)=0
(2sin²(x)-1)(2sin(x)+1)=0

2sin²(x)=1
sin(x)=±1/(√2)

x=Ï€/4
x=Ï€-(Ï€/4)=3Ï€/4
x=-Ï€/4=-Ï€/4+2Ï€=7Ï€/4
x=Ï€-(-Ï€/4)=5Ï€/4

2sin(x)+1=0
sin(x)=-1/2
x=-Ï€/6=-Ï€/6+2Ï€=11Ï€/6
x=Ï€-(-Ï€/6)=Ï€+Ï€/6=7Ï€/6

x=Ï€/4, 3Ï€/4, 7Ï€/4, 5Ï€/4, 11/6, 7Ï€/6

[quote=Mathematician]The thing is I don't quite know what to do with those numbers since the given secant equation is dilated and stuff.[/quote]

It doesn't matter.

Secant is 1/cos(x), making secant undefined at values x = pi/2 + 2kpi

When does (pi/6)*(x-1) equal a value that makes secant undefined on the interval from -12<x<12?

Or more simply, when does (pi/6)*(x-1) = pi/2 or 3pi/2

[quote=Ness]#1: Hint: When is secant undefined?[/quote]

The thing is I don't quite know what to do with those numbers since the given secant equation is dilated and stuff.

#1: Hint: When is secant undefined?

This is why im failing math this year QQ