The Three Primary Trigonometric Functions
Tip: Windows
95 and later come with a Calculator applet that can do everything we need.
The calculator is normally found in the Programs > Accessories folder of
the Start Menu.
 After starting the Calculator applet, select
Scientific from the View menu to make the
trigonometry functions available.
Everything that follows assumes that we will be working with Right
Triangles.
There are three primary trig functions, Sine, Cosine and
Tangent (SIN, COS and TAN on most calculators). These terms were created to scare school children back in the
day when educators thought that fear was an effective teaching tool. If
you are still reading, then you're about to find out how simple these functions
are.
The above three functions each do essentially the
same thing — divide the length of one side of a triangle by
the length of another side. That's all there is to it.
Your average right
triangle. 
Sine Ø = the length of the
opposite side of the
triangle divided by the length of the hypotenuse.
Sine Ø = Opposite ÷ Hypotenuse
Tangent Ø = the length of the opposite side of the triangle divided by the length of the adjacent side.
Tangent Ø = Opposite ÷ Adjacent
Cosine Ø = the length of the adjacent side
of the triangle divided by the length of the hypotenuse.
Cosine Ø = Adjacent ÷ Hypotenuse

Confused? All you
need is a calculator that has trigonometry functions and it is one key press.
Enter
the angle, press the appropriate function and out pops the number.
How to Remember
Trigonometric Functions
Thanks to Graham P. for providing the following method to help remember
the three primary trigonometric functions:
Some 
Sine = 
Old 
Opposite ÷ 
Horse 
Hypotenuse 
Caught 
Cosine = 
Another 
Adjacent ÷ 
Horse 
Hypotenuse 
Trotting 
Tangent = 
On 
Opposite ÷ 
Asphalt 
Adjacent 

For
example, if you want to know the Sine of 5° then enter 5 into the calculator and press the SIN
key. Your calculator should display 0.0871557 give or take some decimal
places. Basic algebra solves the rest (one equation, one
unknown).
The above works only when you know the angle. If you know the lengths
of sides of the triangle but not the angle itself then you can use the Arc functions
to find it.
Arc functions turn the number from the trigonometric function (Sine, Cosine
or Tangent) back into the angle. These functions are Arcsin,
Arctan and Arccos (noted as SIN^{1}, TAN^{1}
or COS^{1} on most calculators).
For example, lets say you are given the
measurement to
prop up the wing tips for the correct
dihedral.
You know the wing span and the amount the tips are propped up which are two
sides of the triangle. Divide the height the wing tip is propped up by half the
wing span, and that is the Sine of the dihedral angle. Now put that number
in your calculator, press Arcsin (SIN^{1}) and the calculator will
display the angle.
