The [b]parity[/b] of a function says whether a function is even, odd or neither.[br][br]To review:[br][br]A function is [b]odd[/b] if [math]f(-x)=-f(x)[/math][br]Odd functions have origin symmetry.[br][br]A function is [b]even[/b] if [math]f(-x)=f(x)[/math][br]Even functions have [math]y[/math]-axis symmetry.
Using the graph above, since [math]P[/math] is on the unit circle, it has coordinates: [math]\left(\cos\theta,\sin\theta\right)[/math][br][br]Consider [math]P'[/math], on the terminal side of [math]-\theta[/math]. Drag [math]P[/math] around the circle and see what you can say about the relationship between [math]P[/math] and [math]P'[/math].
[math]\sin\left(-\theta\right)=[/math]
[math]-\sin\theta[/math][br]So sine is an [b]odd[/b] function.
[math]\cos\left(-\theta\right)=[/math]
[math]-\cos\theta[/math][br]So cosine is an [b]even [/b]function.
[math]\tan\left(-\theta\right)=[/math]
[math]=\frac{\sin\left(-\theta\right)}{\cos\left(-\theta\right)}=\frac{-\sin\theta}{\cos\theta}=-\tan\theta[/math][br]So tangent is an [b]odd [/b]function.
What about the reciprocal functions?
These will follow their reciprocals[br][br]Cosecant is [b]odd[/b]: [math]\csc\left(-\theta\right)=-\csc\theta[/math][br][br]Secant is [b]even[/b]: [math]\sec\left(-\theta\right)=\sec\theta[/math][br][br]Cotangent is [b]odd[/b]: [math]\cot\left(-\theta\right)=-\cot\theta[/math]