91Ó°ÊÓ

Find the angle \(\theta\) between the vectors. $$\begin{aligned}&\mathbf{u}=\cos \left(\frac{\pi}{3}\right) \mathbf{i}+\sin \left(\frac{\pi}{3}\right) \mathbf{j}\\\&\mathbf{v}=\cos \left(\frac{3 \pi}{4}\right) \mathbf{i}+\sin \left(\frac{3 \pi}{4}\right) \mathbf{j} \end{aligned}$$

Find a unit vector in the direction of the given vector. Verify that the result has a magnitude of 1. $$\mathbf{u}=\langle 3,0\rangle$$

Use Heron's Area Formula to find the area of the triangle. $$a=2.5, \quad b=10.2, \quad c=9$$

Finding the Area of a Triangle In Exercises \(39-46\) find the area of the triangle having the indicated angle and sides.\(C=120^{\circ}, \quad a=4, \quad b=6\)

Writing a Complex Number in Standard Form Write the standard form of the complex number. Then represent the complex number graphically. $$9.75\left[\cos \left(280^{\circ} 30^{\prime}\right)+i \sin \left(280^{\circ} 30^{\prime}\right)\right]$$

Use Heron's Area Formula to find the area of the triangle. $$a=75.4, \quad b=52, \quad c=52$$

Find the angle \(\theta\) between the vectors. $$\begin{aligned}&\mathbf{u}=\cos \left(\frac{\pi}{4}\right) \mathbf{i}+\sin \left(\frac{\pi}{4}\right) \mathbf{j}\\\&\mathbf{v}=\cos \left(\frac{\pi}{2}\right) \mathbf{i}+\sin \left(\frac{\pi}{2}\right) \mathbf{j} \end{aligned}$$

Find a unit vector in the direction of the given vector. Verify that the result has a magnitude of 1. $$\mathbf{u}=\langle 0,-2\rangle$$

Find a unit vector in the direction of the given vector. Verify that the result has a magnitude of 1. $$\mathbf{v}=\langle-2,2\rangle$$

Find the area of the triangle having the indicated angle and sides. \(A=150^{\circ}, \quad b=8, \quad c=10\)