### Practice Test

Convert $\mathrm{\xe2\u02c6\u2019620\xc2\xb0}$ to radians.

Find the length of a circular arc with a radius 12 centimeters subtended by the central angle of $\mathrm{30\xc2\xb0}.$

Find the area of the sector with radius of 8 feet and an angle of $\frac{5\mathrm{\xcf\u20ac}}{4}$ radians.

Find the angle between $\mathrm{0\xc2\xb0}$ and $\text{360\xc2\xb0}$ that is coterminal with $\mathrm{375\xc2\xb0}.$

Find the angle between 0 and $2\mathrm{\xcf\u20ac}$ in radians that is coterminal with $\xe2\u02c6\u2019\frac{4\mathrm{\xcf\u20ac}}{7}.$

Draw the angle $\xe2\u02c6\u2019\frac{\mathrm{\xcf\u20ac}}{6}$ in standard position on the Cartesian plane.

A carnival has a Ferris wheel with a diameter of 80 feet. The time for the Ferris wheel to make one revolution is 75 seconds. What is the linear speed in feet per second of a point on the Ferris wheel? What is the angular speed in radians per second?

Find the exact value of $\mathrm{sin}\phantom{\rule{0.3em}{0ex}}\frac{\mathrm{\xcf\u20ac}}{6}.$

State the domain of the sine and cosine functions.

Find the exact value of $\mathrm{cot}\phantom{\rule{0.3em}{0ex}}\frac{\mathrm{\xcf\u20ac}}{4}.$

Find the exact value of $\mathrm{tan}\phantom{\rule{0.3em}{0ex}}\frac{\mathrm{\xcf\u20ac}}{3}.$

Use reference angles to evaluate $\mathrm{csc}\phantom{\rule{0.3em}{0ex}}\frac{7\mathrm{\xcf\u20ac}}{4}.$

If $\text{csc}\phantom{\rule{0.3em}{0ex}}t=1.68,$ what is the $\text{csc}(\xe2\u02c6\u2019t)?$

If $\text{cos}\phantom{\rule{0.3em}{0ex}}t=\frac{\sqrt{3}}{2},$ find $\text{cos}(t\xe2\u02c6\u20192\mathrm{\xcf\u20ac}).$

Which trigonometric functions are even?

Find the missing angle: $\mathrm{cos}\left(\frac{\mathrm{\xcf\u20ac}}{6}\right)=\mathrm{sin}\left(\_\_\_\right)$

Find the missing sides of the triangle $ABC:\mathrm{sin}\phantom{\rule{0.3em}{0ex}}B=\frac{3}{4},c=12$

The angle of elevation to the top of a building in Chicago is found to be 9 degrees from the ground at a distance of 2000 feet from the base of the building. Using this information, find the height of the building.