Analytic

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

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15. tan 2 0 cot 0 16. 1 - sin 2 0 cos 2 0 2 1 - tan2 0 1 - tan 0 1 + tan 0 ' Solve the following equations for 0 < 0 < 2 π: 17. sin 2 0 = i λ/3" 18. cos 2 0 = - -^- . 19. 1 - 2 sin2 2 0 = h (Show two methods). 20. 2 cos2 0 — 1 = - 2. (Show two methods). 21. sin (2 0 + Ή 22. tan (l 0 - ^ j = 1. Λ= - i 23. (sin 2 0 - 1) (sin 0 + 1) = 0. 24. 2 sin2 ( | ) - 3 sin (JA +1=0. 25. 2 cos2 2 0 + 3 sin 2 0 - 3 = 0 . 26. tan2 2 0 - 2 tan 2 0 + 1 = 0. 27. \ Λ + sin 2 0 = cos 2 0. 28. sin 0 + cos 0 = 1.

Sin 0 1 + cos 0 —^—Ξ~ = 2 cos 0. -JΛ + 1 + cos 0 sin 0 22. 1 — tan2 0 _ cos 0 — sin 0 1 + tan~0 ~ cos 0 * 23. tan 0 — sin 0 sec 0 sin8 0 1 + cos 0 ' 24. 7. Functions of Special Angles Angles whose terminal sides fall on the boundaries of the quadrants are called quadrantal angles. Example 1. Find the functions * * . ( ! ) . 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.

Cos 60° 39' 6. sin 77° 17' Interpolate to find the value of each from Table III: 8. 7' 7. 6' 9. 3' 10. 8' 11. 6' 12. 1' 13. 7' 14. 7' Find the reference angle Θ from Table III: 15. 41204 16. 61160 17. 36894 18. 48521 Interpolate to find the reference angle 0 from Table III: 19. 32850 20. 4191 21. 94258 22. 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.

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