91Ó°ÊÓ

Use a calculator to find the acute angle whose corresponding ratio is given. Round to the nearest 10 th of a degree. $$\sin A=0.9063$$

Use the symmetry of the circle and reference ares as needed to state the exact value of the trig functions for the given real number, without the use of a calculator. A diagram may help. a. \(\tan \pi\) b. \(\tan 0\) c. \(\tan \left(\frac{\pi}{2}\right)\) d. \(\tan \left(\frac{3 \pi}{2}\right)\)

State the quadrant of the terminal side of \(\theta,\) using the information given. $$\tan \theta < 0, \sin \theta > 0$$

Circumscribed polygons: The area of a regular polygon circumscribed about a circle of radius \(r\) is given by \(A=n r^{2} \tan \left(\frac{\pi}{n}\right),\) where \(n\) is the number of sides \((n \geq 3)\) and \(r\) is the radius of the circle. Given \(r=10 \mathrm{cm}\) a. What is the area of the circle? b. What is the area of the polygon when \(n=4 ?\) Why? c. Calculate the area of the polygon for \(n=10,20,30,\) and \(100 .\) What do you notice?

Use the formula for area of a circular sector to find the value of the unknown quantity: \(A=\frac{1}{2} r^{2} \theta\). $$A=1080 \mathrm{mi}^{2} ; r=60 \mathrm{mi}$$

Tidal waves: Tsunamis, also known as tidal waves, are ocean waves produced by earthquakes or other upheavals in the Earth's crust and can move through the water undetected for hundreds of miles at great speed. While traveling in the open ocean, these waves can be represented by a sine graph with a very long wavelength (period) and a very small amplitude. Tsunami waves only attain a monstrous size as they approach the shore, and represent a very different phenomenon than the ocean swells created by heavy winds over an extended period of time. A heavy wind is kicking up ocean swells approximately \(10 \mathrm{ft}\) high (from crest to trough), with wavelengths of \(250 \mathrm{ft}\). (a) Find the equation that models these swells. (b) Graph the equation. (c) Determine the height of a wave measured \(200 \mathrm{ft}\) from the trough of the previous wave. (IMAGE CANNOT COPY)

Using the cofunction relationship and the following exact forms: \(\sec 75^{\circ}=\sqrt{6}+\sqrt{2} ; \tan 75^{\circ}=2+\sqrt{3}\) $$\sqrt{6} \csc 15^{\circ}$$

Convert the following degree measures to radians in exact form, without the use of a calculator. $$\theta=30^{\circ}$$

Convert the following degree measures to radians in exact form, without the use of a calculator. $$\theta=-120^{\circ}$$

Angle of elevation: For a person standing \(100 \mathrm{m}\) from the center of the base of the Eiffel Tower, the angle of elevation to the top of the tower is \(71.6^{\circ}\) How tall is the Eiffel Tower?