Ch. 4 - Laws of Sines and Cosines; Vectors
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- In Exercises 1–12, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. If no triangle exists, state 'no triangle.' If two triangles exist, solve each triangle. C = 50°, a = 3, c = 1
Problem 7
- In Exercises 5–8, each expression is the right side of the formula for cos (α - β) with particular values for α and β. b. Write the expression as the cosine of an angle. 5π π 5π π cos ------- cos -------- + sin -------- sin ------- 12 12 12 12
Problem 7
- In Exercises 5–8, each expression is the right side of the formula for cos (α - β) with particular values for α and β. c. Find the exact value of the expression. 5π π 5π π cos ------- cos -------- + sin -------- sin ------- 12 12 12 12
Problem 7
- In Exercises 1–8, use the given vectors to find v⋅w and v⋅v. v = 5i, w = j
Problem 7
- In Exercises 5–12, sketch each vector as a position vector and find its magnitude. v = i - j
Problem 7
- In Exercises 5–8, let v = -5i + 2j and w = 2i - 4j Find the specified vector, scalar, or angle. projᵥᵥv
Problem 8
- In Exercises 1–12, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. If no triangle exists, state 'no triangle.' If two triangles exist, solve each triangle. A = 162°, b = 11.2, c = 48.2
Problem 8
- In Exercises 9–16, let u = 2i - j, v = 3i + j, and w = i + 4j. Find each specified scalar. u ⋅ (v + w)
Problem 9
- In Exercises 5–12, sketch each vector as a position vector and find its magnitude. v = -6i - 2j
Problem 9
- In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 5, b = 7, C = 42°
Problem 9
- In Exercises 9–16, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. A = 56°, C = 24°, a = 22
Problem 10
- In Exercises 9–16, let u = 2i - j, v = 3i + j, and w = i + 4j. Find each specified scalar. u ⋅ v + u ⋅ w
Problem 11
- In Exercises 5–12, sketch each vector as a position vector and find its magnitude. v = -4i
Problem 11
- In Exercises 1–12, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. If no triangle exists, state 'no triangle.' If two triangles exist, solve each triangle. B = 37°, a = 12.4, b = 8.7
Problem 11
- In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. b = 5, c = 3, A = 102°
Problem 11
- In Exercises 9–16, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. A = 85°, B = 35°, c = 30
Problem 12
- In Exercises 9–16, let u = 2i - j, v = 3i + j, and w = i + 4j. Find each specified scalar. (4u) ⋅ v
Problem 13
- In Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j. P₁ = (-4, -4), P₂ = (6, 2)
Problem 13
- In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 6, c = 5, B = 50°
Problem 13
- In Exercises 14–19, use a sum or difference formula to find the exact value of each expression. cos(45° + 30°)
Problem 14
- In Exercises 9–16, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. B = 5°, C = 125°, b = 200
Problem 14
- In Exercises 9–16, let u = 2i - j, v = 3i + j, and w = i + 4j. Find each specified scalar. 4(u ⋅ v)
Problem 15
- In Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j. P₁ = (-8, 6), P₂ = (-2, 3)
Problem 15
- In Exercises 13–16, find the area of the triangle having the given measurements. Round to the nearest square unit. a = 2 meters, b = 4 meters, c = 5 meters
Problem 15
- In Exercises 9–24, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. a = 5, c = 2, B = 90°
Problem 15
- In Exercises 9–16, solve each triangle. Round lengths to the nearest tenth and angle measures to the nearest degree. B = 80°, C = 10°, a = 8
Problem 16
- In Exercises 13–16, find the area of the triangle having the given measurements. Round to the nearest square unit. a = 2 meters, b = 2 meters, c = 2 meters
Problem 16
- Use one or more of the six sum and difference identities to solve Exercises 13–54. In Exercises 13–24, find the exact value of each expression. cos(135° + 30°)
Problem 17
- In Exercises 17–22, find the angle between v and w. Round to the nearest tenth of a degree. v = 2i - j, w = 3i + 4j
Problem 17
- In Exercises 13–20, let v be the vector from initial point P₁ to terminal point P₂. Write v in terms of i and j. P₁ = (-1, 7), P₂ = (-7, -7)
Problem 17