By Isaac Todhunter

This Elibron Classics e-book is a facsimile reprint of a 1864 variation by means of Macmillan and Co., Cambridge and London.

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**Extra resources for A Treatise On The Differential Calculus with numerous examples**

**Example text**

See Fig. 45 Fig. 3. (See Fig. 0Њ. 2 Fig. 68. (See Fig. 18Њ. 90 Fig. 4 (NOTE: See App. 1, Geometry, for properties used in Probs. 4 and the base angles are 48Њ40Ј. Find the equal sides and the altitude of the triangle. In Fig. 5, BD is perpendicular to AC and bisects it. 6 Fig. 10 Considering the earth as a sphere of radius 3960 mi, find the radius r of the 40th parallel of latitude. Refer to Fig. 6. In the right triangle OCB, / OBC ϭ 40Њ and OB ϭ 3960. 7660) ϭ 3033. 53. To three significant digits, the radius r of the 40th parallel is 3030 mi.

The third side is found by using a definition of a second trigonometric function or by using the Pythagorean theorem (see App. 1, Geometry). 2 Four-Place Tables of Trigonometric Functions App. 01-rad intervals. Tables published in texts differ in several ways, such as in the number of digits listed, the number of decimal places in each value, whether or not secant and cosecant values are listed, and the measurement unit of the angles. The angles in Tables 1 and 2 are listed in the left- and right-hand columns.

4 Trigonometric Function Values For many application problems, values of trigonometric functions are needed for angles that are not special angles. These values may be found in tables of trigonometric functions or by using a scientific calculator. 15 illustrate a number of simple applications of trigonometric functions. For these problems, a two-decimal-place table is included below. 04 When using a calculator to find values for trigonometric functions, be sure to follow the procedure indicated in the instruction manual for your calculator.