91Ó°ÊÓ

Finding the Angle Between Two Vectors In Exercises \(31-40,\) find the angle \(\theta\) between the vectors. $$\begin{aligned} \mathbf{u} &=\cos \left(\frac{\pi}{4}\right) \mathbf{i}+\sin \left(\frac{\pi}{4}\right) \mathbf{j} \\ \mathbf{v} &=\cos \left(\frac{\pi}{2}\right) \mathbf{i}+\sin \left(\frac{\pi}{2}\right) \mathbf{j} \end{aligned}$$

Writing a Complex Number in Standard Form In Exercises \(31-40\) , write the standard form of the complex number. Then represent the complex number graphically. $$9.75\left[\cos \left(280^{\circ} 30^{\prime}\right)+i \sin \left(280^{\circ} 30^{\prime}\right)\right]$$

Finding a Unit Vector In Exercises \(39-48,\) find a unit vector in the direction of the given vector. Verify that the result has a magnitude of 1 . $$\mathbf{u}=\langle 0,-2\rangle$$

Finding a Unit Vector In Exercises \(39-48,\) find a unit vector in the direction of the given vector. Verify that the result has a magnitude of 1 . $$\mathbf{v}=\langle- 2,2\rangle$$

Finding the Area of a Triangle In Exercises \(39-46\) find the area of the triangle having the indicated $$A=150^{\circ}, \quad b=8, \quad c=10$$

Using Heron's Area Formula use Heron's Area Formula to find the area of the triangle. $$ a=12.32, \quad b=8.46, \quad c=15.05 $$

Finding the Angle Between Two Vectors In Exercises \(41-44\) , graph the vectors and find the degree measure of the angle \(\theta\) between the vectors. $$\mathbf{u}=3 \mathbf{i}+4 \mathbf{j}$$ $$\mathbf{v}=-7 \mathbf{i}+5 \mathbf{j}$$

Writing a Complex Number in Standard Form In Exercises \(41-44,\) use a graphing utility to write the complex number in standard form. $$5\left(\cos \frac{\pi}{9}+i \sin \frac{\pi}{9}\right)$$

Finding a Unit Vector In Exercises \(39-48,\) find a unit vector in the direction of the given vector. Verify that the result has a magnitude of 1 . $$\mathbf{v}=\langle 5,-12\rangle$$

Finding the Angle Between Two Vectors In Exercises \(41-44\) , graph the vectors and find the degree measure of the angle \(\theta\) between the vectors. $$\mathbf{u}=6 \mathbf{i}+3 \mathbf{j}$$ $$\mathbf{v}=-4 \mathbf{i}+4 \mathbf{j}$$