Respuesta :

Pasta0
So We Know That tan(x) Equals

[tex] \tan(x) = \frac{ \sin(x) }{ \cos(x) } [/tex]
We Can Use Logic, We Know That Anything That Makes The Denominator 0, Will Not Work, So We Need To Know What Makes Sin(x) equal to 0 and Cos(x) equal to 1 or -1 BUT NOT 0

[tex] \sin(0) = 0 \: \cos(0) = 1 \\ \sin(180) = 0 \: \cos(180) = - 1 \\ \sin(360) = 0 \: \cos(360) = 1 \\ \sin( - 180) = 0 \: \cos( - 180) = - 1 \\ \sin( - 360) = 0 \: \cos( - 360) = 1[/tex]
[tex] \cos(90) = 0 \\ \cos( - 90) = 0 \\ \cos(270) = 0 \\ \cos( - 270) = 0[/tex]
We Didn't Want Cosine To equal Zero Because Then We Get

[tex] \tan(x) = \frac{ \sin(x) }{ \cos(x) } \\ \tan(x) = \frac{ \sin(90) }{ \cos(90) } \\ \tan(x) = \frac{1}{0} \\ \tan(x) = indeterminate[/tex]

THE ANSWER IS C : -360°,-180°,0°,180°,360°

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