By Heidi A. Howard

ISBN-10: 0321227379

ISBN-13: 9780321227379

Instructor's options handbook to accompany Trigtonometry, eighth variation by means of Lial, Hornsby, Schneider

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**Sample text**

Thus, cot (θ + 180° ) is negative. 81. 90° < θ < 180° ⇒ −90° > −θ > −180° ⇒ −180° < −θ < −90°, so −θ lies in quadrant III ( −180° is coterminal with 180° and −90° is coterminal with 270°. ). Thus, cos ( −θ ) is negative. 82. Answers will vary. Chapter 1: Review Exercises 1. The complement of 35° is 90° − 35° = 55°. The supplement of 35° is 180° − 35° = 145°. 2. −51° is coterminal with 360° + ( −51° ) = 309°. 3. − 174° + 360° = 186° 4. 792° is coterminal with 792° - 2(360°) = 72° 5. Let n represent any integer.

Y1 is sin x and Y2 is tan x. 7321 sin 90° = 1 tan 90° : undefined 51. Since sin 60° = 50. Y1 is cos x and Y2 is csc x. 1547 cos 90° = 0 csc 90° = 1 3 and 60° is between 0° and 90°, A = 60°. 2 52. 7071067812 is a rational approximation for the exact value 2 (an irrational value). 2 2 2 53. 70710678). This corresponds to the point , . 2 2 These coordinates are the sine and cosine of 45°. 54. ( ) The line passes through ( 0, 0 ) and 1, 3 . The slope is change in y over the change in 3 x.

B; 480° − 360° = 120° and 180° − 120° = 60° (120° is in quadrant II) 2 is a good choice for r because in a 30° − 60° right triangle, the hypotenuse is twice the length of the shorter side (the side opposite to the 30° angle). By choosing 2, one avoids introducing a fraction (or decimal) when determining the length of the shorter side. Choosing any even positive integer for r would have this result; however, 2 is the most convenient value. 8. – 9. Answers will vary. θ sin θ cos θ tan θ cot θ sec θ csc θ 10.

### Trigonometry by Heidi A. Howard

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