How do you graph $theta=(5pi)/4$ ?

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Answer 1 · 2016-11-01T19:15:53

It is the line $y = x; x < 0$

This the 3rd quadrant, therefore, we must restrict x and y to be less than 0 , when we substitute $tan^-1(y/x)$ for $theta$

$tan^-1(y/x) = (5pi)/4; x < 0 and y < 0$

Take the tangent of both sides:

$tan(tan^-1(y/x)) = tan((5pi)/4); x < 0 and y < 0$

The tangent "undoes" its inverse and substitute 1 for $tan((5pi)/4)$ :

$y/x = 1; x < 0 and y < 0$

Multiply both sides by x:

$y = x; x < 0$

We dropped the restriction on y, because it is, now, a dependent variable.

How do you graph theta=(5pi)/4theta=(5pi)/4?