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SAMPLE Final (200 points Total) Math 240 Professor O. LePoint Instructions: Answer the following questions without notes or the book. You can use calculators. Complete as many questions within 2 hours. Partial credit can be given for each section. Question 1: Give the definition for the following in the space provided below: • Vertical Asymptotes of y = tan x • Supplementary Angles • Reference Angle • SOH CAH TOA • Inverse Function Name________________ Student ID____________ Question 2: Convert 18° to π radians and find 2 coterminal angles in radians. Show all work. Question 3: The following two triangles are similar. Find x and y. Hint: Draw the triangles separately. Your answers will be in variables. X -2y 10 74° X-5 X +y 20 74° Question 4: Solve sin2 θ + 3sin θ + 2 = 0. Question 5: Give all the solutions for θ. Solve 2 sin x + (sin2 x + cos2 x ) = 0 Question 6: What is the sine, cosine, and tangent values of θ in standard position if the terminal side of θ is defined by x+2y =0, for x≥ 0. Box your answers. (15 points) Name________________ Student ID____________ Question 7: Give the fractions for the following trigonometric functions using the figure. Give the restrictions. If θ = tan -1 u θ • Sin θ = __________________________________ • cos θ = __________________________________ • cot θ = __________________________________ Question 8 : Give the exact value of the expression without using a calculator cos ( tan -1 5/12 - tan -1 3/4 ). Question 9: Write sin 2θ – sin 4θ as a product of two functions. Name________________ Student ID____________ Question 10: Use the half angle identity to find cos (-22.5°). Question 11: Show [ HINT: start with the left side, and multiply top and bottom by the same expression.) Remember to FOIL. ] 1 sin x cos x cos x 1 sin x Question 12 : Graphing y = 2 sin (2x) + 1 • What is the period of y = 2 sin (2x) + 1 ? • Evaluate y = 2 sin (2x) + 1 , on an interval starting with 0 and ending with π. • Sketch y = 2 sin (2x) + 1 in the space provided below 3 2 1 2 0 4 3 4 3 4 Name________________ Student ID____________ CONTINUED Question 13 : • After seeing the lectures, what basic math topic, which was once very confusing, is easier to understand now? • What teaching methods helped you understand the difficult concepts better? • What were your original expectations of Trigonometry? • Do you plan to take more math classes? If so, what classes? • What surprises did you encounter in this class? Name________________ Student ID____________ CONTINUED Question 14: The Hubble telescope traveling in a circular orbit 1600 km above the surface of the Earth takes 2 hours to make an orbit. The radius of earth is 6400 km. 1600 6400 • Find the linear speed of the telescope. Show all work and equations. • Find the distance the telescope travels in 4.5 hours. Show all work and equations. Question 15: Graph y= sin x Y=arccos x on the same graph Name________________ Student ID____________ CONTINUED Question 15: Prove the following Question 16: Prove the following Question 17: Perform the Following