Sine
Domain  (âˆž,âˆž) 
Range  [1,1] 
Value at x=0  0 
Maxima*  $\left ( \left ( 2k+\frac{1}{2} \right )\pi,1 \right )$ 
Minima*  $\left ( \left ( 2k\frac{1}{2} \right )\pi ,1 \right ) $ 
Root*  $k\pi $ 
Critical Point*  $k\pi \frac{\pi }{2} $ 
Inflection Point*  $k\pi $ 
* Variable $k$ is an integer
Domain and Range are only given for real (not complex) numbers
The sine function is commonly remembered to be opposite over hypotenuse which can be written as $\displaystyle \sin\left ( \alpha \right )=\frac{opposite}{hypotenuse}=\frac{a}{h}$ . The sine function is commonly used to model periodic phenomena such as sound and light waves, the position and velocity of harmonic oscillators, sunlight intensity and day length, and average temperature variations throughout the year. Relation to Slope The trigonometric functions can be defined in terms of the rise, run, and slope of a line segment relative to some horizontal line.

Unlike the definitions with the right or left triangle or slope, the angle can be extended to the full set of real arguments by using the unit circle. This can also be achieved by requiring certain symmetries and that sine be a periodic function.
Cosine
Domain  (âˆž,âˆž) 
Range  [1,1] 
Value at x=0  1 
Maxima*  $\left ( 2\pi k,1 \right )$ 
Minima*  $\left (\pi+ 2\pi k,1 \right )$ 
Root*  $\frac{\pi}{2}+\pi k$ 
Critical Point*  $\pi k$ 
Inflection Point*  $\frac{\pi}{2}+\pi k$ 
* Variable $k$ is an integer
Domain and Range are only given for real (not complex) numbers
The cosine function is commonly remembered to be adjacent over hypotenuse which can be written as $\displaystyle \sin\left ( \alpha \right )=\frac{adjacent}{hypotenuse}=\frac{b}{h}$ . Like the sine function, it is commonly used to model periodic phenomena such as sound and light waves, the position and velocity of harmonic oscillators, sunlight intensity and day length, and average temperature variations throughout the year. 
Sine & Cosine Together
Sine and cosine are a great team. The rest of the trigonometric functions can be written as complex sine and cosine functions, which you will see in the coming weeks.
The basic relationship between the sine and the cosine is the Pythagorean trigonometric identity which can be written as $\sin^2\left ( \theta \right )+\cos^2\left ( \theta \right )=1$ . We could go and show the various identities of sine and cosine functions, but we figured you can Google them or go to http://en.wikipedia.org/wiki/List_of_trigonometric_identities and see them.