College trigonometry by William Le Roy Hart

By William Le Roy Hart

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The letter in parentheses is the independent variable. The letter at the left of the parentheses is merely a convenient name letter or abbreviation for the function. " If f(x) is a function of x and h is a particular value for x, then f(h) represents the value of f(x) when x = h. (1) [any function of (8 + 3600)J = (same function of 8); [any function ILLUSTRATION1. If f(x) = 3x2 + 2x - 7, then f(2) = 3(22) + 2(2) + 2( - 3) - 7 = 14. ILLUSTRATION 2. If f(x) = sin xO,then f(90) = sin 90° = 1. Similarly, a function of two independent variables x and y may be represented by F(x, V), G(x, V), etc.

Hence, we obtain the following reduction formulas: ILLUSTRATION Proof of (1). 1. sin ( 1. Let - 27°) = /3 = - O. We add, for which the functions . see (- 8) = see 8j cot (- 8) = - cot O. 4540. (Table VII) Then,t for a case where () >0 involved will exist. This proviso is understood In all* future cases where trigonometric identities are described. t The statements of the proof hold for any angle (j although drawn. The student should draw other figures. a special figure is 72 FUNDAMENTAL CHARACTERISTICS OF THE FUNCTIONS Figure 47 shows {3 and y PI FIG.

A 150-pound shell for a battery of artillery is dragged up a runway inclined 42° to the horizontal. Find the pressure of the shell against the runway and the force required to drag the shell. 2. A truck weighing 6875 pounds moves up a bridge inclined 7° 32' from the horizontal. Find the pressure of the truck against the bridge. 3. An automobile weighing 2600 pounds stands on a hill inclined 25° 36' from the horizontal. How large a force must be counteracted by the brakes of the automobile to prevent it from rolling downhill?

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