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Use the sine and cosine ratios to find the values of x and y .

x 80. y 80. cos 40° = Use sine and cosine. sin 40° =. x = 80(cos 40°) Solve for the variable. y = 80(sin 40°). Use a calculator. y. x. Because point M is in the third quadrant, both coordinates are negative. To the nearest tenth, OM  –61.3,–51.4 . Vectors.

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Use the sine and cosine ratios to find the values of x and y .

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  1. x 80 y 80 cos 40° = Use sine and cosine. sin 40° = x = 80(cos 40°) Solve for the variable.y = 80(sin 40°) Use a calculator.y x Because point M is in the third quadrant, both coordinates are negative. To the nearest tenth, OM–61.3,–51.4. Vectors LESSON 8-6 Additional Examples Describe OM as an ordered pair. Give coordinates to the nearest tenth. Use the sine and cosine ratios to find the values of x and y. Quick Check

  2. Vectors LESSON 8-6 Additional Examples Use compass directions to describe the direction of the vector. The angle is measured from due south toward east. Because the vector forms a 22° angle with the south segment, it is 22° east of south. Quick Check

  3. Draw a diagram to represent the situation. d = (12 – 0)2 + (–9 – 0)2 Distance Formula Simplify. d = 144 + 81 Simplify. d = 225 Take the square root. d = 15 Vectors LESSON 8-6 Additional Examples A boat sailed 12 mi east and 9 mi south. The trip can be described by the vector 12, –9. Use distance and direction to describe this vector a second way. To find the distance sailed, use the Distance Formula.

  4. 9 12 tan x° = = 0.75 Use the tangent ratio. x = tan–1 (0.75) Find the angle whose tangent is 0.75. 0.75 Use a calculator. Vectors LESSON 8-6 Additional Examples (continued) To find the direction the boat sails, find the angle that the vector forms with the x-axis. The boat sailed 15 mi at about 37° south of east. Quick Check

  5. To find the first coordinate of s, add the first coordinates of v and w. To find the second coordinate of s, add the second coordinates of v and w. s = 4, 3 = 4, –3 Add the coordinates. = 4 + 4, 3 + (–3) Simplify. = 8, 0 Vectors LESSON 8-6 Additional Examples Vectors v4, 3 and w4, –3 are shown below. Write s, their sum, as an ordered pair. Quick Check

  6. Draw a diagram to represent the situation. c2 = 2502 + 202 The lengths of the legs are 250 and 20. c2 = 62,900 Simplify. Use a calculator. c Vectors LESSON 8-6 Additional Examples An airplane’s speed is 250 mi/h in still air. The wind is blowing due east at 20 mi/h. If the airplane heads directly north, what is its resultant speed and direction? The diagram shows the sum of the two vectors. To find the resultant speed, use the Pythagorean Theorem.

  7. 20 250 Use the tangent ratio. tan x° = = 0.08 x = tan–1 (0.08) Use the inverse of the tangent. Use a calculator. x Vectors LESSON 8-6 Additional Examples Quick Check (continued) To find the direction of the airplane’s flight, use trigonometry to find x. The airplane’s speed is about 251 mi/h. Its direction is about 5° east of north.

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