Trigonometry.
Trigonometry is that portion of geometry which has for its object the measurement of triangles. When it treats of plane triangles, it is called Plane Trigonometry; and as the engineer will continually meet in his studies of higher mathematics the terms used in plane trigonometry, it is advantageous for him to become familiar with some of the principles and definitions relating to this branch of mathematics.
The circumferences of all circles contain the same number of degrees, but the greater the radius the greater is the absolute measures of a degree. The circumference of a fly wheel or the circumference of the earth have the same number of degrees; yet the same number of degrees in each and every circumference is the measure of precisely the same angle.
The circumference of a circle is supposed to be divided into 360 degrees or divisions, and as the total angularity about the center is equal to four right angles, each right angle contains 90 degrees, or 90°, and half a right angle contains 45°. Each degree is divided into 60 minutes, or 60′; and for the sake of still further minuteness of measurement, each minute is divided into 60″. In a whole circle there are, therefore, 360 × 60 × 60 = 1,296,000 seconds. The annexed diagram, [fig. 136], exemplifies the relative positions of the
Sine,
Co-sine,
Versed Sine,
Tangent,
Co-Tangent,
Secant and
Co-secant
of an angle.
Fig. 136.
These may be defined thus: