State 3 differences between $f(\theta) = \cos\theta$, and $f(\theta) = \sin\theta$. I can't think of any other difference besides the $x$- and $y$-intercepts. 
For example, the length of one wave cycle (360 degrees) for the function $f(\theta) = \cos\theta$ will intersect the $y$-axis at $(0,1)$ and the $x$-axis at $(90,0)$, and $(270,0)$. 
The function $f(\theta) = \sin\theta$ will intersect $(0,0)$, $(180,0)$, and $(360,0)$ in the length of one wave cycle.
Is there any other differences between the two sinusoidal functions? 
 A: Just for more information:
i) They also have different derivatives. $$\frac{\mathrm{d}}{\mathrm{d}\theta} \sin \theta = \cos \theta \qquad \qquad \frac{\mathrm{d}}{\mathrm{d}\theta} \cos \theta = - \sin \theta$$
ii) They have different series expansions: $$\sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots \\ \cos x = 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \cdots $$
(The $\sin $ expansion only has odd powers and factorials, and $\cos $'s only has evens. Coincidence?)
iii) They are both related to complex numbers by $$e^{ix} = \cos x + i \sin x $$
One is the real part and the other one is the imaginary part.
iv) A nicer way to talk about the intercept is to notice that both graphics are equal modulo a horizontal shift of $\frac{\pi}{2}$, that is: $$\cos \left(x - \frac{\pi}{2} \right) = \sin x $$
A: $cos\theta$ is even and $sin\theta$ is odd.
A: Here's another: $$\cos (-\theta)=\cos\theta\quad\color{grey}{\rm and }\quad\sin(-\theta)=-\sin\theta.$$
So the $\cos$ function is even, and the $\sin$ function is odd.
