Ch. 4 - Laws of Sines and Cosines; Vectors
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- In Exercises 43–44, use the given measurements to solve the following triangle. Round lengths of sides to the nearest tenth and angle measures to the nearest degree. a = 400, b = 300
Problem 44
- In Exercises 39–46, find the unit vector that has the same direction as the vector v. v = i + j
Problem 45
- In Exercises 45–50, determine whether v and w are parallel, orthogonal, or neither. v = 3i - 5j, w = 6i - 10j
Problem 45
- In Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given. ||v|| = 6, θ = 30°
Problem 47
- In Exercises 45–50, determine whether v and w are parallel, orthogonal, or neither. v = 3i - 5j, w = 6i + 10j
Problem 47
Problem 48
Write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given.
||v|| = 8, θ = 45°
- In Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given. ||v|| = 12, θ = 225°
Problem 49
- In Exercises 45–50, determine whether v and w are parallel, orthogonal, or neither. v = 3i - 5j, w = 6i + 18 j 5
Problem 49
Problem 50
Write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given.
||v|| = 10, θ = 330°
- In Exercises 47–52, write the vector v in terms of i and j whose magnitude ||v|| and direction angle θ are given. ||v|| = 1/2, θ = 113°
Problem 51
- In Exercises 53–56, let u = -2i + 3j, v = 6i - j, w = -3i. Find each specified vector or scalar. 4u - (2v - w)
Problem 53
- In Exercises 53–56, let u = -2i + 3j, v = 6i - j, w = -3i. Find each specified vector or scalar. ||u + v||² - ||u - v||²
Problem 55
- In Exercises 57–64, find the exact value of the following under the given conditions: a. cos (α + β) 3 5 sin α = ------ , α lies in quadrant I, and sin β = ------- , β lies in quadrant II. 5 13
Problem 57
- In Exercises 57–64, find the exact value of the following under the given conditions: a. cos (α + β) 3 1 tan α = ﹣ ------ , α lies in quadrant II, and cos β = ------- , β lies in quadrant I. 4 3
Problem 59
- In Exercises 57–64, find the exact value of the following under the given conditions: a. cos (α + β) 8 1 cos α = ------ , α lies in quadrant IV, and sin β = ﹣------- , β lies in quadrant III. 17 2
Problem 61
- In Exercises 61–64, find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v. v = -10i + 15j
Problem 61
Problem 62
Find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v.
v = 2i - 8j
- In Exercises 57–64, find the exact value of the following under the given conditions: a. cos (α + β) 3 3𝝅 1 3𝝅 tan α = ------ , 𝝅 < α < -------- , and cos β = ------- , ---------- < β < 2𝝅. 4 2 4 2
Problem 63
- In Exercises 61–64, find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v. v = (4i - 2j) - (4i - 8j)
Problem 63
Problem 64
Find the magnitude ||v||, to the nearest hundredth, and the direction angle θ, to the nearest tenth of a degree, for each given vector v.
v = (7i - 3j) - (10i - 3j)
- In Exercises 69–74, rewrite each expression as a simplified expression containing one term. cos (α + β) cos β + sin (α + β) sin β
Problem 69