13) The angle of elevation to the top of a building in Baltimore is found to be \(4\) degrees from the ground at a distance of \(1\) mile from the base of the building. Using this information, find the height of the building.
Practice Test
1) Convert \( \dfrac{5π}{6}\) radians to degrees.
- Answer
-
\(150°\)
2) Convert \(−620°\) to radians.
3) Find the length of a circular arc with a radius \(12\) centimeters subtended by the central angle of \(30°\).
- Answer
-
\(6.283\) centimeters
4) Find the area of the sector with radius of \(8\) feet and an angle of \(\dfrac{5π}{4}\) radians.
5) Find the angle between \(0°\) and \(360°\) that is coterminal with \(375°\).
- Answer
-
\(15°\)
6) Find the angle between \(0\) and \(2π\) in radians that is coterminal with \(−\dfrac{4π}{7}\).
7) Draw the angle \(315°\) in standard position on the Cartesian plane.
- Answer
-
8) Draw the angle \(−\dfrac{π}{6}\) in standard position on the Cartesian plane.
9) 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?
- Answer
-
\(3.351\) feet per second, \( \dfrac{2π}{75}\) radians per second
10) Find the exact value of \( \sin \dfrac{π}{6}\).
11) Compute sine of \(240°\).
- Answer
-
\(−\dfrac{\sqrt{3}}{2}\)
12) State the domain of the sine and cosine functions.
13) State the range of the sine and cosine functions.
- Answer
-
\([ –1,1 ]\)
14) Find the exact value of \( \cot \dfrac{π}{4}\).
15) Find the exact value of \( \tan \dfrac{π}{3}\).
- Answer
-
\( \sqrt{3}\)
16) Use reference angles to evaluate \( \csc \dfrac{7π}{4}\).
17) Use reference angles to evaluate \( \tan 210°\).
- Answer
-
\(\dfrac{\sqrt{3}}{3}\)
18) If \( \csc t=0.68\), what is the \( \csc (−t)\)?
19) If \( \cos t= \dfrac{\sqrt{3}}{2}\), find \( \cos (t−2π)\).
- Answer
-
\(\dfrac{\sqrt{3}}{2}\)
20) Which trigonometric functions are even?
21) Find the missing angle: \(\cos \left(\dfrac{\pi }{6} \right)= \sin (\;)\)
- Answer
-
\(\dfrac{π}{3}\)
22) Find the missing sides of the triangle \( ABC: \sin B= \dfrac{3}{4},c=12\)
23) Find the missing sides of the triangle.
- Answer
-
\(a=\dfrac{9}{2},b=\dfrac{9\sqrt{3}}{2}\)
24) 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.