Co/Sine Properties

This is a post summarizing the basic properties of the cosine and sine functions.


Here is the cosine function and its properties:

In this example:
h is 0;
k and L are 3;
b and P are 2π and
a is 2.










And here is the sine function and its properties:

In this example:
h is -π/2;
k and L are 3;
b and P are π and
a is 2.










The parameter h is rather simple, as its affect doesn't change throughout the various functions we've learned this year. The a, b and k parameters and the new parts like the period and the line of oscillation (the middle or mid-point of the function) are different. They can be determined by the naked eye or with these formulas:

The "M" and "m" in this case are the "maximum" and "minimum" of the function in question. Notice that L and k have the same formula, so it isn't necessary to find both as finding one will automatically find the other.


Don't let yourself get fooled by the period and frequency in this example for they are not the same. Frequency is how long a function is (from the beginning of the tulip/snake to the end of it) and the period is the amount of 2π-segments within the whole frequency. It just so happens that this example has a frequency of 1, which is why we do not see a b in the functions stated in the example images.

Here are two additional formulas you may find useful:

Thank-you and please share your thoughts in the comments section! :)