Chapter 6

In Exercises 5-20, use the Law of Cosines to solve the triangle. Round your answers to two decimal places. \(B = 75^{\circ}20'\), \(a = 6.2\), \(c = 9.5\)

In Exercises 5-24, use the Law of Sines to solve the triangle.Round your answers to two decimal places. \(B\ =\ 28^{\circ}\), \(C\ =\ 104^{\circ}\), \(a\ =\ 3\frac{5}{8}\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(1 - \sqrt{3}i\)

In Exercises 15-24, use the vectors \(\mathbf{u} = \langle 3, 3 \rangle\), \(\mathbf{v} = \langle -4, 2 \rangle\), and \(\mathbf{w} = \langle 3, -1 \rangle\) to find the indicated quantity. State whether the result is a vector or a scalar. \((\mathbf{u} \cdot \mathbf{v}) \mathbf{v}\)

In Exercises 5-20, use the Law of Cosines to solve the triangle. Round your answers to two decimal places. \(B = 125^{\circ}40'\), \(a = 37\), \(c = 37\)

In Exercises 5-24, use the Law of Sines to solve the triangle.Round your answers to two decimal places. \(A\ =\ 36^{\circ}\), \(a\ =\ 8\), \(b\ =\ 5\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(4 - 4\sqrt{3}i\)

In Exercises 15-24, use the vectors \(\mathbf{u} = \langle 3, 3 \rangle\), \(\mathbf{v} = \langle -4, 2 \rangle\), and \(\mathbf{w} = \langle 3, -1 \rangle\) to find the indicated quantity. State whether the result is a vector or a scalar. \((\mathbf{v} \cdot \mathbf{u}) \mathbf{w}\)

In Exercises 5-20, use the Law of Cosines to solve the triangle. Round your answers to two decimal places. \(C = 15^{\circ}15'\), \(a = 7.45\), \(b = 2.15\)

In Exercises 5-24, use the Law of Sines to solve the triangle.Round your answers to two decimal places. \(A\ =\ 60^{\circ}\), \(a\ =\ 9\), \(c\ =\ 10\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(-2(1 + \sqrt{3}i)\)

In Exercises 15-24, use the vectors \(\mathbf{u} = \langle 3, 3 \rangle\), \(\mathbf{v} = \langle -4, 2 \rangle\), and \(\mathbf{w} = \langle 3, -1 \rangle\) to find the indicated quantity. State whether the result is a vector or a scalar. \((3\mathbf{w} \cdot \mathbf{v}) \mathbf{u}\)

In Exercises 13-24, find the component form and the magnitude of the vector \(\mathbf{v}\).'' Initial Point - \((-3, -5)\) Terminal Point - \((5, 1)\)

In Exercises 5-20, use the Law of Cosines to solve the triangle. Round your answers to two decimal places. \(C = 43^{\circ}\), \(a = \frac{4}{9}\), \(b = \frac{7}{9}\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(\frac{5}{2}(\sqrt{3} - i)\)

In Exercises 15-24, use the vectors \(\mathbf{u} = \langle 3, 3 \rangle\), \(\mathbf{v} = \langle -4, 2 \rangle\), and \(\mathbf{w} = \langle 3, -1 \rangle\) to find the indicated quantity. State whether the result is a vector or a scalar. \((\mathbf{u} \cdot 2\mathbf{v}) \mathbf{w}\)

In Exercises 13-24, find the component form and the magnitude of the vector \(\mathbf{v}\).'' Initial Point - \((-2, 7)\) Terminal Point - \((5, -17)\)

In Exercises 5-20, use the Law of Cosines to solve the triangle. Round your answers to two decimal places. \(C = 101^{\circ}\), \(a = \frac{3}{8}\), \(b = \frac{3}{4}\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(-5i\)

In Exercises 13-24, find the component form and the magnitude of the vector \(\mathbf{v}\).'' Initial Point - \((1, 3)\) Terminal Point - \((-8, -9)\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(12i\)

In Exercises 15-24, use the vectors \(\mathbf{u} = \langle 3, 3 \rangle\), \(\mathbf{v} = \langle -4, 2 \rangle\), and \(\mathbf{w} = \langle 3, -1 \rangle\) to find the indicated quantity. State whether the result is a vector or a scalar. \(1-\) ||\(\mathbf{u}\)||

In Exercises 13-24, find the component form and the magnitude of the vector \(\mathbf{v}\).'' Initial Point - \((1, 11)\) Terminal Point - \((9, 3)\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(-7 + 4i\)

In Exercises 15-24, use the vectors \(\mathbf{u} = \langle 3, 3 \rangle\), \(\mathbf{v} = \langle -4, 2 \rangle\), and \(\mathbf{w} = \langle 3, -1 \rangle\) to find the indicated quantity. State whether the result is a vector or a scalar. \((\mathbf{u} \cdot \mathbf{v}) - (\mathbf{u} \cdot \mathbf{w})\)

In Exercises 13-24, find the component form and the magnitude of the vector \(\mathbf{v}\).'' Initial Point - \((-1, 5)\) Terminal Point - \((15, 12)\)

In Exercises 5-24, use the Law of Sines to solve the triangle.Round your answers to two decimal places. \(A\ =\ 110^{\circ}15'\), \(a\ =\ 48\), \(b\ =\ 16\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(3 - i\)

In Exercises 15-24, use the vectors \(\mathbf{u} = \langle 3, 3 \rangle\), \(\mathbf{v} = \langle -4, 2 \rangle\), and \(\mathbf{w} = \langle 3, -1 \rangle\) to find the indicated quantity. State whether the result is a vector or a scalar. \((\mathbf{v} \cdot \mathbf{u}) - (\mathbf{w} \cdot \mathbf{v})\)

In Exercises 13-24, find the component form and the magnitude of the vector \(\mathbf{v}\).'' Initial Point - \((-3, 11)\) Terminal Point - \((9, 40)\)

In Exercises 5-24, use the Law of Sines to solve the triangle.Round your answers to two decimal places. \(C\ =\ 95.20^{\circ}\), \(a\ =\ 35\), \(c\ =\ 50\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(2\)

In Exercises 25-30, use the dot product to find the magnitude of \(\mathbf{u}\). \(\mathbf{u} = \langle -8, 15 \rangle\)

In Exercises 25-34, use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. \(A\ =\ 110^{\circ}\), \(a\ =\ 125\), \(b\ =\ 100\)

In Exercises 25-30, use the dot product to find the magnitude of \(\mathbf{u}\). \(\mathbf{u} = \langle 4, -6 \rangle\)

In Exercises 25-34, use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. \(A\ =\ 110^{\circ}\), \(a\ =\ 125\), \(b\ =\ 200\)

Represent the complex number graphically, and find the trigonometric form of the number. $$2 \sqrt{2}-i$$

In Exercises 25-30, use the dot product to find the magnitude of \(\mathbf{u}\). \(\mathbf{u} = 20\mathbf{i} + 25\mathbf{j}\)

In Exercises 27-32, determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve the triangle. \(a = 8\), \(c = 5\), \(B = 40^{\circ}\),

In Exercises 25-34, use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. \(A\ =\ 76^{\circ}\), \(a\ =\ 18\), \(b\ =\ 20\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(-3 - i\)

In Exercises 27-32, determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve the triangle. \(a = 10\), \(b = 12\), \(C = 70^{\circ}\),

In Exercises 25-34, use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. \(A\ =\ 76^{\circ}\), \(a\ =\ 34\), \(b\ =\ 21\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(5 + 2i\)

In Exercises 25-30, use the dot product to find the magnitude of \(\mathbf{u}\). \(\mathbf{u} = 6\mathbf{j}\)

In Exercises 25-34, use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. \(A\ =\ 58^{\circ}\), \(a\ =\ 11.4\), \(b\ =\ 12.8\)

In Exercises 15-32, represent the complex number graphically, and find the trigonometric form of the number. \(8 + 3i\)

In Exercises 25-30, use the dot product to find the magnitude of \(\mathbf{u}\). \(\mathbf{u} = -21\mathbf{i}\)

In Exercises 27-32, determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle. Then solve the triangle. \(a = 11\), \(b = 13\), \(c = 7\),

In Exercises 25-34, use the Law of Sines to solve (if possible) the triangle. If two solutions exist, find both. Round your answers to two decimal places. \(A\ =\ 58^{\circ}\), \(a\ =\ 4.5\), \(b\ =\ 12.8\)