Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
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