Editing Inverse trigonometric functions (section)

=== Finding the angle of a right triangle ===
[[Image:Trigonometry triangle.svg|right|thumb|A [[right triangle]] with sides relative to an angle at the <math>A</math> point.]]
Inverse trigonometric functions are useful when trying to determine the remaining two angles of a [[right triangle]] when the lengths of the sides of the triangle are known. Recalling the right-triangle definitions of sine and cosine, it follows that

:<math>\theta = \arcsin \left( \frac{\text{opposite}}{\text{hypotenuse}} \right) = \arccos \left( \frac{\text{adjacent}}{\text{hypotenuse}} \right) .</math>

Often, the hypotenuse is unknown and would need to be calculated before using arcsine or arccosine using the [[Pythagorean Theorem]]: <math>a^2+b^2=h^2</math> where <math>h</math> is the length of the hypotenuse. Arctangent comes in handy in this situation, as the length of the hypotenuse is not needed.

:<math>\theta = \arctan \left( \frac{\text{opposite}}{\text{adjacent}} \right) \, .</math>

For example, suppose a roof drops 8 feet as it runs out 20 feet. The roof makes an angle ''θ'' with the horizontal, where ''θ'' may be computed as follows:

:<math>\theta
= \arctan \left( \frac{\text{opposite}}{\text{adjacent}} \right)
= \arctan \left( \frac{\text{rise}}{\text{run}} \right)
= \arctan \left( \frac{8}{20} \right) \approx 21.8^{\circ} \, .</math>