Download θ θ )π π π

Math 1250 Exam 3 Review Chapter 4.1-6.3
This review does not include everything that may be on the exam.
1. Evaluate exactly without using a calculator.
⎛ 11π ⎞
a. csc⎜ −
⎟
⎝ 4 ⎠
b. sin 300 D
c. sec 750 D
2. The graph shown is one period of a function of the form y = A sin ( Bx − C ) . Write
the equation for this function.
4
2
2
4
6
8
10
12
-2
-4
3. The radius of a wheel rolling on the ground is 80 centimeters. If the wheel rotates
D
through an angle of 60 , how many centimeters does it move? Express your
answer in terms of π and then round to two decimal places.
4. Given that sin θ = − 13 and tanθ > 0 , calculate the other five trigonometric
functions exactly.
5. Find the amplitude, period, and phase shift of y = π sin(πx + π ) and sketch at least
one period of its graph. Label the beginning and end of one period and all
maximum and minimum points.
⎛ 12 5 ⎞
6. If the terminal point determined by t is ⎜ ,− ⎟ , find the exact value of cot t .
⎝ 13 13 ⎠
7. Find θ to the nearest degree.
θ
8
5
12
8. Solve the triangle or triangles. A = 40 , a = 6 , b = 4 .
D
9. Use your calculator to approximate csc 4.2 to 6 decimal places.
8
and if the terminal side of θ lies in quadrant III, find the exact
17
value of tan θ cot θ + cscθ .
10. If cos θ = −
11. In a predator /prey model, the predator population is modeled by the function
y = 8000 + 900 cos 2t where t is measured in years.
a. What is the maximum predator population.
b. Find the length of time between successive periods of the maximum
population.
π⎞
⎛1
12. Sketch at least one period of the function y = csc ⎜ x − ⎟ . Label the beginning
2⎠
⎝2
and end of the period and draw in all vertical asymptotes with dashed lines.
13. Verify the identity
1 + sin t
= tan 2 t + 1 + tan t sec t .
2
cos t
14. Find the exact value of
5π
12
D
b. sin 22.5
5
4
15. If tan α = , α lies in quadrant III, tan β =
, and β lies in quadrant I, find
3
12
cos (α − β ) .
16. Find all solutions to 2sin x + 1 = 0 .
17. Solve each equation on the interval [ 0, 2π ) .
a. tan
a. cos x − 2cos x = 3
2
b. tan
x
= −1
2
⎡
−1
⎛
18. Find the exact value of the expression tan ⎢cos ⎜ −
⎣⎢
⎝
3 ⎞⎤
⎟⎥ .
2 ⎠ ⎦⎥
5π ⎞
⎟ and find its rectangular coordinates.
4 ⎠
20. Convert the polar equation r cosθ = −1 into a rectangular equation.
⎛
⎝
19. Plot the polar coordinate ⎜ −2,
21. Solve the following right triangle.
c = 18.6 ft.
β = 27 . 9 D
a
α
b