Why are the tangents for 90 and 270 degrees undefined?

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kokheleka36tx · Accepted Answer

You can also say that             tan      x        =                  sin        x                    cos        x            .You can take a look at the overlap of sinx and cosx below to see what happens to each as we approach             90      o       and             270      o       from the right or left:graph{(y - sinx)(y - cosx) = 0 [-0.034, 6.2831, -1.2, 1.2]} We can establish that:            lim              x        →                  90                                    o                              -                                                                        sin        x                    cos        x              =    -          1      0        =    -    ∞  because cos x decreases while sin x increases as       x    →          90      o       from the left, and            lim              x        →                  90                                    o                              +                                                                        sin        x                    cos        x              =          1      0        =    ∞  because both cos x and sin x increase as       x    →          90      o       from the right.We can also see that:            lim              x        →                  270                                    o                              -                                                                        sin        x                    cos        x              =    -          1      0        =    -    ∞  because sin x decreases but cos x increases as       x    →          270      o       from the left, and            lim              x        →                  270                                    o                              +                                                                        sin        x                    cos        x              =          1      0        =    ∞  because both sin x and cos x decrease as       x    →          270      o       from the right.Tan x of those angles is undefined because the limits from the left and right sides are not the same.

Why are the tangents for 90 and 270 degrees undefined?

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