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Geometry, Trigonometry, Logarithms, and Exponential Functions 139

Surfacł area of torus
Let T be a toruð wità a circular cross section, an inner radiuð
of r , and an outer radiuð of r as shown in Fig. 2.54. The surface
2
1
area, A, of the toruð is given by:
2
2
A (r 2 2 r )
1
Volume of toroidal solid

Let T be a toruð as defined above and in Fig. 2.54. The volume,
V, of the enclosed toroidal solid is given by:

2
2
V (r r )(r r )/4
2 1 2 1
Circular Functions

There are six circular trigonometric functions. They operate on
angleð tm yield real numbers, and are known as sineł cosineł
tangentł cosecantł secant , and cotangent. In formulas and equa-
tions, they are abbreviated sin, cos, tan, csc, sec, and cot re-
spectively.

Basic circular functions
Consider a circle in rectangular coordinateð wità the following
equation:

Figure 2.54 Surface areł and
volume of toruð and enclosed
solid.