1. Copyright © 1999 by the McGraw-Hill Companies, Inc. Barnett/Ziegler/Byleen College Algebra with Trigonometry, 6 th Edition Chapter Eight Additional Topics in Trigonometry

2. sin  a =  b =  c The law of sines is generally used to solve the ASA, AAS, and SSA cases for oblique triangles. Law of Sines 8-1-85

3. aNumber of  (h = b sin  )trianglesFigure Acute 0 < a < h0 Acute a = h1 Acute h < a < b2 SSA Variations 8-1-86-1

4. aNumber of  (h = b sin  )trianglesFigure Acute a  b1 Obtuse 0 < a  b0 Obtuse a > b1 SSA Variations 8-1-86-2

5. All three equations say essentially the same thing Law of Cosines 8-2-87

6. Tail-to-tip Rule Parallelogram Rule Vector Addition 8-3-88

7. Algebraic Properties of Vectors 8-4-89

8. Polar Graphing Grid 8-5-90

9. r 2 = x 2 + y 2 sin  = y r or y = r sin  cos  = x r or x = r cos  tan  = y x Polar–Rectangular Relationships 8-5-91

10. Standard Polar Graphs—I Line through origin: Vertical line: Horizontal line:  = a r = a/cos  = a sec  r = a/sin  = a cos  (a) (b) (c) 8-5-92-1

11. Standard Polar Graphs—I Circle: Circle: Circle: r = a r = a cos  r = a sin  (d) (e)(f) 8-5-92-2

12. Cardioid: Cardioid: Three-leaf rose: r = a + a cos  r = a + a sin  r = a cos 3  (g)(h) (i) Standard Polar Graphs—II 8-5-93-1

13. Four-leaf rose: Lemniscate: Archimedes' spiral: r = a cos 2  r 2 = a 2 cos 2  r = a  a > 0 (j) (k) (l) Standard Polar Graphs—II 8-5-93-2

14. Complex Plane 8-6-94

15. For n a positive integer greater than 1, r 1/n e (  /n + k 360°/n)i k = 0, 1, …, n – 1 are the n distinct nth roots of re  i and there are no others. The four distinct fourth roots of –1 are: nth-Root Theorem 8-7-95