Pre-Exam. 4 Location of 3. 4 sin 3 ' = b Location of 180 ' = c Location of 315
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1 MATH-330 Pre-Exam Spring 09 Name Rocket Number INSTRUCTIONS: You must show enough work to justify your answer on ALL problems except for Problem 6. Correct answers with no work or inconsistent work shown will not receive full credit. All answers are to be exact; no decimal approximations. You are NOT allowed to use any electronic device for this pre-exam.. For each of the following angles, indicate where the terminal side of the angle is located. Then find the reference angle and the exact value of the indicated trigonometric function for the angle. 5 pts. each a. 4 Location of ' = 4 3 = b. 80 Location of 80 ' = 80 = c. 35 Location of 35 ' = csc 35 =
2 . Find the angle between 0 and that is coterminal with the angle 67 cot. Show how you get your coterminal angle. 6 pts and then find the exact value of 6 Coterminal angle 67 cot = 6 3. Find the angle between and 0 that is coterminal with the angle 55. Show how you get your coterminal angle. 6 pts and then find the exact value of 3 Coterminal angle 55 3 = 4. Find the angle between 0 and 360 that is coterminal with the angle 80 and then find the exact value of sec 80. Show how you get your coterminal angle. 4 pts. Coterminal angle sec 80 =
3 5. Find what quadrant the angle 90 is in. Then find the reference angle of the angle. You need to show your work for finding the reference angle. 5 pts. The angle 90 is in the quadrant and the reference angle is. 6. Find what quadrant the angle is in. Then find the reference angle of the angle. You need to show 4 your work for finding the reference angle. 5 pts. The angle is in the quadrant and the reference angle is Convert the following angles to degrees if it is given in radians or to radians if it is given in degrees. 5 pts. each a. 8 5 Answer b. 65 Answer c. 4 Answer
4 8. If 0 and sec 0, then lies in which quadrant? 5 pts. Answer 9. If the terminal side of passes through the point 4, 7, then find the exact value of sec and. 8 pts. sec = = 0. If the terminal side of is in the III quadrant and lies on the line 5x 6 y 0, find the exact value of and cot. 0 pts. = cot =. Given: 7 Find the exact value of a. = 3 pts. 3 b. csc = 3 pts.
5 . Use a right triangle to find the exact value of sec and if 5 and 0. pts. 4 lies in the quadrant sec = = 3. Given the triangle below, find x. Set up an equation and solve. 4 pts. 45 x 8 x 4. Find the exact angle, where 0 360, if the terminal side of passes through the point 6, 4. 5 pts.
6 5. From the top of a building, which is 80 meters tall, the angle of depression to an object on level ground below is 5.7. How far is the object from the top of the building? Draw a picture and label known information. Indicate any variable you use. Set up an equation and solve. 6 pts. Answer 6. Find the exact value of each of the following. 3 pts. each a. = b. = c. 3 Arc = d. = e. Arc =
7 7. Sketch the graph of two cycles of the following function on the same side of the y-axis. Label the numbers on the x- and y-axes as needed. Label where the cycles begin and end. Then label the numbers between these numbers. 0 pts. 8x 5 y cot Amplitude 3 6 Period Phase Shift 8. Sketch the graph of two cycles of the following function on the same side of the y-axis. Label the numbers on the x- and y-axes as needed. Label where the cycles begin and end. 6 pts. 4 y sec x Amplitude 9 6 Period Phase Shift
8 3 9. Find the exact value of sec 8 8 pts. 3 3 is in quadrant sec 8 8 = 0. Use one Pythagorean Identity and Basic Identities to find the exact value of and if 8 and is in the III quadrant. 8 pts. 5 = =. Find all the exact solutions in degrees of the equation csc 0. 8 pts. Put a box around your answers.
9 . Find the exact value of pts. Put a box around your answer. 3. Find the exact value of and if 7 3 cot and. 8 pts. 3 is in quadrant 4. Find the exact value of = 5. 5 pts. Put a box around your answer. 8 =
10 5. Find all the solutions in degrees to the equation 3x 3 in the interval [ 80, 80]. 9 pts. Put a box around your answers. 6. Sketch the graph of two cycles of the following function on the same side of the y-axis. Label the numbers on the x- and y-axes as needed. Label where the cycles begin and end. Then label the numbers between these numbers. 0 pts. y 3 7 x Amplitude Period Phase Shift
11 FORMULAS sec cot csc
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