Which two cases can be solved using the Law of Sines?

Fill in the blank(s). The projection of u onto v is given by $\operatorname{proj}_{\mathrm{v}} \mathbf{u}=$ ________.

In given exercise, represent the complex number graphically, and find the standard form of the number.

$$\frac{3}{2}\left(\cos 330^{\circ}+i \sin 330^{\circ}\right)$$

Represent the complex number graphically, and find the standard form of the number. $5\left(\cos 135^{\circ}+i \sin 135^{\circ}\right)$

The Leaning Tower of Pisa in Italy leans because it was built on unstable soil-a mixture of clay, sand, and water. The tower is approximately 58.36 meters tall from its foundation. The top of the tower leans about 5.45 meters off center.

(a) Find the angle of lean $\alpha$ of the tower.

(b) Write $\beta$ as a function of $d$ and $\theta$, where $\theta$ is the angle of elevation to the sun.

(c) Use the Law of Sines to write an equation for the length $d$ of the shadow cast by the tower in terms of $\theta$.

(d) Use a graphing utility to complete the table.

Determine whether u and v are orthogonal, parallel, or neither.

$$\begin{array}{l} \mathbf{u}=-\frac{3}{5} \mathbf{i}+\frac{7}{10} \mathbf{j} \\ \mathbf{v}=12 \mathbf{i}-14 \mathbf{j} \end{array}$$

Represent the complex number graphically, and find the standard form of the number. $6\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right)$

use the value of the trigonometric function to evaluate the indicated functions. sin t = 4/5 , sin (t + π)

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. $\mathbf{v}=8 \mathbf{i}-15 \mathbf{j}$

Find a unit vector in the direction of the given vector. Verify that the result has a magnitude of 1. $w = −7i$

Represent the complex number graphically, and find the standard form of the number. $2\left(\cos 120^{\circ}+i \sin 120^{\circ}\right)$

Forces of 60 pounds and 100 pounds have a resultant force of 125 pounds. Find the angle between the two forces.

Determine whether u and v are orthogonal, parallel, or neither.

$$\begin{array}{l} \mathbf{u}=\langle 15,9\rangle \\ \mathbf{v}=\langle-5,-3\rangle \end{array}$$