For problems #1-15, evaluate each trigonometric expression. Your answer should be in exact form where possible.
1) \(\cos (30 ^{\circ})\)
2) \(\sin (45 ^{\circ})\)
3) \(\tan \left (\Large\frac{5 \pi}{6}\right)\)
4) \(\sec \left(\Large\frac{4 \pi}{3}\right)\)
5) \(\cot \left(\Large\frac{7 \pi}{4}\right)\)
6) \(\csc\left(2\pi\right)\)
7) \(\tan \left(\Large\frac{9 \pi}{4}\right)\)
8) \(\cos \left(\Large\frac{\pi}{2}\right)\)
9) \(\csc (150 ^{\circ})\)
10) \(\sec (210 ^{\circ})\)
11) \(\tan \left(\Large\frac{\pi}{2}\right)\)
12) \(\sin \left(\Large\frac{3 \pi}{2}\right)\)
13) \(\cot (420 ^{\circ})\)
14) \(\cos (0)\)
15) \(\cot \left(-\Large\frac{\pi}{2}\right)\)
For problems #16-20, a point on the terminal side of an angle is given. List all six trigonometric values of the angle.
16) \((-3,4)\)
17) \((7,-2)\)
18) \((1,4)\)
19) \((-8,0)\)
20) \((-17,-17)\)
Review
21) Hadley is looking up at the top of a building. The angle of elevation from Hadley's eyes to the top of the building is \(54 ^{\circ}\), if Hadley is \(22\) feet away from the base of the building and her eye's are \(5\) feet off the ground, how tall is the building? Round your answer to the nearest hundredth of a foot.
22) Solve the equation, \(\log_{2} x +\log_{2} (x-4) =5\).
23) In a movie theater there are \(8\) seats in the first row, the number of seats in each row increases by \(2\) as you move away from the first row. If there are \(14\) rows in the theater how many total seats are there?
24) Give an example of a geometric series that converges.
25) Find the inverse function of \(f(x) = 3 e^{4x-1}\).
Solution Bank
1) \(\cos (30 ^{\circ})\)
2) \(\sin (45 ^{\circ})\)
3) \(\tan \left (\Large\frac{5 \pi}{6}\right)\)
4) \(\sec \left(\Large\frac{4 \pi}{3}\right)\)
5) \(\cot \left(\Large\frac{7 \pi}{4}\right)\)
6) \(\csc\left(2\pi\right)\)
7) \(\tan \left(\Large\frac{9 \pi}{4}\right)\)
8) \(\cos \left(\Large\frac{\pi}{2}\right)\)
9) \(\csc (150 ^{\circ})\)
10) \(\sec (210 ^{\circ})\)
11) \(\tan \left(\Large\frac{\pi}{2}\right)\)
12) \(\sin \left(\Large\frac{3 \pi}{2}\right)\)
13) \(\cot (420 ^{\circ})\)
14) \(\cos (0)\)
15) \(\cot \left(-\Large\frac{\pi}{2}\right)\)
For problems #16-20, a point on the terminal side of an angle is given. List all six trigonometric values of the angle.
16) \((-3,4)\)
17) \((7,-2)\)
18) \((1,4)\)
19) \((-8,0)\)
20) \((-17,-17)\)
Review
21) Hadley is looking up at the top of a building. The angle of elevation from Hadley's eyes to the top of the building is \(54 ^{\circ}\), if Hadley is \(22\) feet away from the base of the building and her eye's are \(5\) feet off the ground, how tall is the building? Round your answer to the nearest hundredth of a foot.
22) Solve the equation, \(\log_{2} x +\log_{2} (x-4) =5\).
23) In a movie theater there are \(8\) seats in the first row, the number of seats in each row increases by \(2\) as you move away from the first row. If there are \(14\) rows in the theater how many total seats are there?
24) Give an example of a geometric series that converges.
25) Find the inverse function of \(f(x) = 3 e^{4x-1}\).
Solution Bank