91Ó°ÊÓ

Use a calculator to evaluate the trigonometric functions for the indicated angle values. Round your answers to four decimal places. $$\cot 55^{\circ}$$

Use a calculator to evaluate the trigonometric functions for the indicated angle values. Round your answers to four decimal places. $$\cot 29^{\circ}$$

Convert from radians to degrees. Round your answers to the nearest hundredth of a degree. $$3.27$$

Convert from radians to degrees. Round your answers to the nearest hundredth of a degree. $$-2.7989$$

Solve the triangle \(\alpha=120^{\circ}, a=7,\) and \(b=9\) Solution: Use the Law of sines to find \(\beta .\) \(\frac{\sin \alpha}{a}=\frac{\sin \beta}{b}\) Let \(\alpha=120^{\circ}, a=7\) and \(b=9\). \(\frac{\sin 120^{\circ}}{7}=\frac{\sin \beta}{9}\) Solve for \(\sin \beta\). \(\sin \beta=1.113\) Solve for \(\beta\). \(\beta=42^{\circ}\) Sum the angle measures to \(180^{\circ}\). \(120^{\circ}+42^{\circ}+\gamma=180^{\circ}\) Solve for \(\gamma\). \(\gamma=18^{\circ}\) Use the Law of sines to find \(c\). \(\frac{\sin \alpha}{a}=\frac{\sin \gamma}{c}\) Let \(\alpha=120^{\circ}, a=7\) and \(\gamma=18^{\circ}\). \(\frac{\sin 120^{\circ}}{7}=\frac{\sin 18^{\circ}}{c}\) Solve for \(c\). \(c=2.5\) \(\alpha=120^{\circ}, \beta=42^{\circ}, \gamma=18^{\circ}, a=7, b=9,\) and \(c=2.5\) This is incorrect. The longest side is not opposite the longest angle. There is no triangle that makes the original measurements work. What mistake was made?

A plane flew \(\mathrm{N} 30^{\circ} \mathrm{W}\) at 350 mph for 3 hours. \(\mathrm{A}\) second plane starts at the same point and takes off at the same time. It is known that after 3 hours, the two planes are 2100 miles apart. Find the original bearing of the second plane, to the nearest hundredth of a degree.

A 40-foot slide leaning against the bottom of a building's window makes a \(55^{\circ}\) angle with the building. The angle formed with the building by the line of sight from the top of the window to the point on the ground where the slide ends is \(40^{\circ} .\) How tall is the window? (IMAGE CANNOT COPY)

Evaluate the following expressions exactly: $$\cos 240^{\circ}$$

State in which quadrant or on which axis each angle with the given measure in standard position would lie. $$270^{\circ}$$

Evaluate the following expressions exactly: $$\cot \left(-315^{\circ}\right)$$