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 [b][i]r[/i] = distance from [color=#666666]point [i]P[/i][/color] to the origin. [/b] [br][br]If this is the case, recall [math]cos\left(\theta\right)=\frac{x}{r}[/math] and [math]sec\left(\theta\right)=\frac{r}{x}[/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!) [br][/b][/color][br]
Regardless of where [color=#666666][b]point [i]P[/i][/b][/color] lies, what relationship can you write about the ratios [math]cos\left(\theta\right)[/math] and [math]cos\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]sec\left(\theta\right)[/math] and [math]sec\left(-\theta\right)[/math]?
What do these 2 observations imply about the cosine and secant functions? (Click [url=https://www.geogebra.org/m/H9BbuSwX]here[/url] and/or [url=https://www.geogebra.org/m/A5S7naz3]here[/url] for a hint!)