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Magazine Problem 58
Find all degree solutions. $$ 3 \sin ^{2} 2 \theta-2 \sin 2 \theta-5=0 $$
Problem 58
Assume vector \(\mathbf{V}\) is in standard position, has the given magnitude, and that \(\theta\) is the angle \(\mathbf{V}\) makes with the positive \(x\)-axis. Write \(\mathbf{V}\) in vector component form \(a \mathbf{i}+b \mathbf{j}\), and approximate your values to two significant digits. $$|\mathbf{V}|=330, \theta=340^{\circ}$$
Problem 59
Find all degree solutions. $$ \sin 4 \theta \cos 2 \theta+\cos 4 \theta \sin 2 \theta=-1 $$
Problem 59
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 60
Find all degree solutions. $$ \cos 3 \theta \cos 2 \theta-\sin 3 \theta \sin 2 \theta=-1 $$
Problem 60
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 61
Solve each equation for \(\theta\) if \(0^{\circ} \leq \theta<360^{\circ}\). \(\sin \theta+\cos \theta=1\)
Problem 61
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 62
Solve each equation for \(\theta\) if \(0^{\circ} \leq \theta<360^{\circ}\). $$ \sin \theta-\cos \theta=0 $$
Problem 62
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. $$\mathbf{F}=-2 \sqrt{3} \mathbf{i}+2 \mathbf{j}$$
