Download e-book for kindle: Analytic Trigonometry by William J. Bruce, W. J. Langford, E. A. Maxwell and I. N.

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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