Sine and Cosine: Overview
The **sine** (abbreviated "**sin**") and cosine
("**cos**") are the two most prominent
trigonometric functions.
All other trig functions can be expressed in terms of them. In fact, the sine
and cosine functions are closely related and can be expressed in terms of
each other.

Definition 1 is the simplest and most intuitive definition of the
sine and cosine function. The sine definition basically says that,
on a right triangle,
the following measurements are related:

- the measurement of one of the non-right angles (q)
- the length of the side opposite to that angle
- the length of the triangle's hypotenuse

Alternately, the cosine definition basically says that,
on a right triangle,
the following measurements are related:

- the measurement of one of the non-right angles (q)
- the length of the side adjacent to that angle
- the length of the triangle's hypotenuse

Futhermore, Definition I gives exact
equations that describe each of these relations:

sin(q) = opposite / hypotenuse

cos(q) = adjacent / hypotenuse

This first equation says that if we evaluate the sine of that angle
q, we will get the exact same value as if we divided the length
of the side **opposite** to that angle by the length of the triangle's
hypotenuse. This second equation says that if we evaluate the cosine of that angle
q, we will get the exact same value as if we divided the length
of the side **adjacent** to that angle by the length of the triangle's
hypotenuse.
These relations holds for any right triangle, regardless
of size.

The main result is this: If we *know* the values of any two of the
above quantities, we can use the above relation to mathematically
*derive* the third quantity. For example, the sine
function allows us to answer any of the following three questions:

"Given a right triangle, where the measurement of one of the
non-right *angles* (q) is known and the length of the
side *opposite* to that angle q is known, __find the
length of the triangle's __*hypotenuse*."

"Given a right triangle, where the measurement of one of the
non-right *angles* (q) is known and the length of the
triangle's *hypotenuse* is known, __find the
length of the side __*opposite* to that angle q."

"Given a right triangle, where the length of the
triangle's *hypotenuse* and the length of
one of the triangle's other sides is known, __find the
measurement of the __*angle* (q) *opposite* to that
other side."

The cosine is similar, except that the adjacent side is used
instead of the opposite side.

The functions takes the forms **y = sin(q)**
and **x = cos(q)**.
Usually, q is an angle measurement and x and y denotes lengths.

The sine and cosine functions, like all trig functions,
evaluate differently depending on the units
on q, such as *degrees, radians, or grads*. For example, sin(90°) = 1, while sin(90)=0.89399....
explaination

Both functions are trigonometric **cofunctions** of each other,
in that function of the complementary angle, which is the "cofunction,"
is equal to the other function:

sin(x) = cos(90°-x) and

cos(x) = sin(90°-x).

Furthermore, sine and cosine are mutually

**orthogonal**.