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Magazine Problem 43
Vector \(\boldsymbol{W}\) is in standard position, and makes an angle of \(230^{\circ}\) with the positive \(x\)-axis. Its magnitude is 8 . Write \(\mathbf{W}\) in component form \(\langle a, b\rangle\) and in vector component form \(a \mathbf{i}+b \mathbf{j}\).
Problem 44
The problems that follow review material we covered in Sections 3.1 and \(6.1\). Solve each equation for \(\theta\) if \(0^{\circ} \leq \theta<360^{\circ}\). If rounding is necessary, round to the nearest tenth of a degree.\(10 \cos ^{2} \theta+\cos \theta-3=0\)
Problem 44
Vector \(\mathbf{F}\) is in standard position, and makes an angle of \(285^{\circ}\) with the positive \(x\)-axis. Its magnitude is 30 . Write \(\mathbf{F}\) in component form \(\langle a, b\rangle\) and in vector component form \(a \mathbf{i}+b \mathbf{j}\).
Problem 45
Find the magnitude of each vector and the angle \(\theta, 0^{\circ} \leq \theta<360^{\circ}\), that the vector makes with the positive \(x\)-axis. $$\mathbf{U}=\langle 3,3\rangle$$
Problem 45
Find \(\theta\) to the nearest tenth of a degree if \(0 \leq \theta<360^{\circ}\), and\(\sin \theta=0.7380\)
Problem 46
Find the magnitude of each vector and the angle \(\theta, 0^{\circ} \leq \theta<360^{\circ}\), that the vector makes with the positive \(x\)-axis. $$\mathbf{V}=\langle 5,-5\rangle$$
Problem 46
Find \(\theta\) to the nearest tenth of a degree if \(0 \leq \theta<360^{\circ}\), and\(\sin \theta=0.2351\)
Problem 47
Find the magnitude of each vector and the angle \(\theta, 0^{\circ} \leq \theta<360^{\circ}\), that the vector makes with the positive \(x\)-axis. $$\mathbf{W}=-\mathbf{i}-\sqrt{3} \mathbf{j}$$
Problem 48
Find the magnitude of each vector and the angle \(\theta, 0^{\circ} \leq \theta<360^{\circ}\), that the vector makes with the positive \(x\)-axis. $$\mathbf{F}=-2 \sqrt{3} \mathbf{i}+2 \mathbf{j}$$
