By Heidi A. Howard
Instructor's suggestions guide to accompany Trigtonometry, eighth version via Lial, Hornsby, Schneider
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Additional info for Trigonometry
We see that cos 45° = sin 45°, so T = 45°. 59. As T increases from 0° to 90°, the cosine decreases and the sine increases. 60. As T increases from 90° to 180°, the cosine decreases and the sine decreases. 4: Using the Definitions of the Trigonometric Functions 27 61. The area of a triangle is 1 bh . The area of one of the six equilateral triangles is the following. 2 3 3 1 1 ( x ) x = x 2 2 2 2 2 3 x 3 3 in the area of a triangle, which gives Since sin θ = 2 = , we can substitute sin θ for 2 x 2 1 2 1 x sin θ .
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. Any angle coterminal with 270° would be 270° + n ⋅ 360°. 6. 320 rotations per min = = 320 60 32 9 rotations per sec = 163 rotations per sec rotations per 2 3 sec = 32 9 ( 360° ) A point on the edge of the pulley will move 1280° in 7.
Step 3: EF = BD = 1 AG EG EG = = = EG. AD EF 1 The height of the tree (in feet) is (approximately) the number of paces. 1: Trigonometric Functions of Acute Angles 1. sin A = side opposite 21 = hypotenuse 29 3. side adjacent 20 = hypotenuse 29 side opposite 21 tan A = = side adjacent 20 sin A = side opposite n = p hypotenuse side adjacent m = p hypotenuse side opposite n tan A = = side adjacent m cos A = 2. sin A = cos A = side opposite 45 = hypotenuse 53 4. side adjacent 28 = hypotenuse 53 side opposite 45 tan A = = side adjacent 28 cos A = sin A = side opposite k = z hypotenuse side adjacent = hypotenuse side opposite tan A = = side adjacent cos A = y z k y For Exercises 5–10, refer to the Function Values of Special Angles chart on page 50 of your text.