8

Trigonometric Functions 145
Note:
Thecompfunctionisanalternativetothe
n o t a t i o n V. x , V. y, V. z .
Special Animation Func tion
Funct ion M ea ni ng
noise(p,q,r) 3D noise: retu rns a randomly
generated p osition
Thearbitraryvaluesp,qandr,areusedasa
random-generation seed. You can reuse these
values to ensure that noise() returns the same
value.
Tr igonometric Functions
This topic is a quick review for readers who need a
reminder about this area of mathematics. If you’re
familiar with trigonometry, you can skip this topic.
If you find this topic difficult to follow, you might
consult a more basic reference on mathematics.
Trigonometric functions are principally used to
model or describe:
• Therelationbetweenanglesinatriangle(hence
the name).
• Rotations about a circle, including locations
giveninpolarcoordinates.
•Cyclicalorperiodicvalues,suchassound
waves.
The three basic trigonometric functions are
derived from an angle rotating about a unit circle.
Tr ig onometric functions based on the u n it circle
The tangent function is undefined for x=0.
Another way to define the target is:
Because XYR defines a ri ght-angled triangle, the
relation between the sine and cosine is:
The graphs of the basic trigonometric functions
illustrate their cyclical nature.
Graphs of basic trigonometric functions
Thesineandcosinefunctionsyieldthesame
values, but t he phase differs along the X axis by
∏/2: in other words, 90 degrees.
Theinversefunctionsforthetrigonometric
functions are the arc functions; the inverse only