CHAPTER 10 143. Introduction Section 1. BASIC TRIGONOMETRIC THEORY a. Definition. Trigonometry deals with the relationships between the sides and angles of triangles. It uses the theories of basic mathematics the numbers of arithmetic, the equations of algebra, and the theorems of geometry -to aid in the measurement of the sides and angles of triangles. b. Application. The ability to use angles and their trigonometric relationships in electrical calculations is especially important in the study of alternating current (ac). Most effects of ac circuit components can be studied or described only in terms of the part of a cycle by which a current lags behind a corresponding voltage, or vice versa. A large percentage of the problems relating to the analysis of ac circuits and communication networks involves the solution of the right triangle in some form. Certain facts about right triangles are familiar (ch 9) -namely, that the square of the hypotenuse is equal to the sum of the squares of the other two sides (c2 = a2 + b2), that the sum of the acute angles of a right triangle is 90°, and that the sum of the interior angles of any triangle is 180°. However, it would be impossible to solve certain problems with only this information. After learning other relationships between the sides and angles of triangles, it will be found that trigonometry is an easy and accurate method of solving many problems in ac electricity (ch 15). 144. Trigonometric Functions a. General. Trigonometry is based on the six trigonometric functions involved in the study of the right angle. If the value of one quantity depends on the value of a second quantity, the first quantity is said to be a function of the second. The six trigonometric functions -sine (sin), cosine (cos), tangent (tan), co tangent (cot), secant (sec), and cosecant (esc) -are derived from the ratios of the sides of a right triangle to each other. b. The Right Triangle. Figure 34 shows a right triangle, with the angles labeled A, B, and C; C is the right angle. The sides of the triangle are labeled a, b, and c, with the side opposite each angle given the same letter as the angle. The following are the trigonometric ratios of the sides of a triangle: If one trigonometric function of a right triangle is known, the other trigonometric functions can be determined. This is done by using the Pythagorean theorem (par. 133). Example 1: Given the right triangle ABC (fig. 23): side a is 4; side C is 9. Since sin A = , find the other trigonometric func |