Suppose [math]\theta[/math] is an angle drawn in standard position. [color=#666666][b]Let [i]P[/i]([i]x[/i], [i]y[/i]) = any point in the coordinate plane[/b][/color], [br]and [i]r[/i] = distance from [color=#666666][b]point [i]P[/i][/b][/color] to the origin, then [br][br][math]tan\left(\theta\right)=\frac{y}{x}[/math]and [math]cot\left(\theta\right)=\frac{x}{y}[/math]. [br][br]Interact with the applet below for a minute or two. Then answer the questions that follow. [br][color=#666666][b](Be sure to move point [i]P[/i] to various locations!) [/b][/color]
Regardless of where [color=#666666][b]point [i]P[/i][/b][/color] lies, what relationship can you write about the ratios [math]tan\left(-\theta\right)[/math]and [math]tan\left(\theta\right)[/math]?
Regardless of where [color=#666666][b]point [i]P[/i][/b][/color] lies, what relationship can you write about the ratios [math]cot\left(-\theta\right)[/math] and [math]cot\left(\theta\right)[/math]?
What do these 2 observations imply about the tangent and cotangent functions? (Click [url=https://www.geogebra.org/m/jpkTfgtk]here[/url] and/or [url=https://www.geogebra.org/m/GY9tNvfB]here[/url] for a hint!)