How do you graph $θ = \frac{5 π}{4}$ $theta=(5pi)/4$ ?

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How do you graph $θ = \frac{5 π}{4}$ $theta=(5pi)/4$ ?

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Answer 1 · 2016-11-01T19:15:53

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

Explanation:

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

${tan}^{- 1} (\frac{y}{x}) = \frac{5 π}{4}; x < 0 and y < 0$ $tan^-1(y/x) = (5pi)/4; x < 0 and y < 0$

Take the tangent of both sides:

$tan ({tan}^{- 1} (\frac{y}{x})) = tan (\frac{5 π}{4}); x < 0 and y < 0$ $tan(tan^-1(y/x)) = tan((5pi)/4); x < 0 and y < 0$

The tangent "undoes" its inverse and substitute 1 for $tan (\frac{5 π}{4})$ $tan((5pi)/4)$ :

$\frac{y}{x} = 1; x < 0 and y < 0$ $y/x = 1; x < 0 and y < 0$

Multiply both sides by x:

$y = x; x < 0$ $y = x; x < 0$

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

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How do you graph $θ = \frac{5 π}{4}$ $theta=(5pi)/4$ ?

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How do you graph $θ = \frac{5 π}{4}$ $theta=(5pi)/4$ ?