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By William J. Bruce, W. J. Langford, E. A. Maxwell and I. N. Sneddon (Auth.)

ISBN-10: 0080103111

ISBN-13: 9780080103112

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Sample text

Sin 0 + cos 0 = 1.

Method 1. Draw 90° in standard position (Fig. 12). Choose a point P (0, 1) on the terminal side. 32 ANALYTIC TRIGONOMETRY Then x = 0, y = 1, r = 1, and we get 1 sin 90° = - = - = 1 r 1 cos 90° = - = - = 0 r 1 v 1 tan 90° = - = - (undefined) cot 90° = - = r = 0 y i r 1 sec 90° = - = - (undefined) x 0 csc 90° = - = = - = 1 *y iy - P{0,1) 0 ^ , I X Flo. 12 FIG. 4* 10 Flo. 13 TRIGONOMETRIC FUNCTIONS OF ANGLES 33 Method 2. Draw an angle Θ in standard position such that Θ is slightly less than 90° (Fig.

83330 23. 8598 24. 11. Solutions of Elementary Trigonometric Equations From the definitions of the trigonometric functions it is evident that a given angle has but one sine, one cosine, one TRIGONOMETRIC FUNCTIONS OF ANGLES 41 tangent, etc. The converse is not true. A given sine may belong to any one of a set of angles. The same is true for the other trigonometric functions. Consider the equation sin 0 = \. We already know that one value of Θ for which this is true is 0 = 30°. However, any angle Θ which has 30° as its reference angle will have a sine equal to \.

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Analytic Trigonometry by William J. Bruce, W. J. Langford, E. A. Maxwell and I. N. Sneddon (Auth.)

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