MATH 1113 Practice Test 5 SPRING 2016
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1 MATH 1113 Practice Test 5 SPRING Solve the right triangle given that 37 and b = 4. (find all the missing parts) Find the area. Solve the right triangle given that 16 and a = 31. (find all the missing parts) Find the area 3. Solve the right triangle given that 74 and c = 3. (find all the missing parts) Find the area Solve the equation. Give all answers between 0, for extra credit sin cos sin 3 1 Verify the identity 7. 1 sin x sec xtan x 8. 1 sin x 3 6. sec sec 1 cot tan sin cos sin 9. An object attached to a coiled spring is pulled down a distance a from its rest position and then released. Assuming that the motion is simple harmonic with frequency f, write an equation that relates the displacement d of the object from its rest position after t seconds. Also assume that the positive direction of the motion is up. a = 5 f = 1 6 seconds 10. If the distance d (in feet) that an object travels in time t (in seconds) is given by the equation d cos(4 t), then a) Describe the motion of the object. b) What is the maximum displacement from its rest position? c) What is the time required for one oscillation? d) What is the frequency? 11. Two homes are located on opposite sides of a small hill. To measure the distance between them, a surveyor walks a distance of 50 feet from house A to point C, uses a transit to measure angle ACB, which is found to be 90 degrees, and then walks to house B, a distance of 60 feet. How far apart are the houses? 1. Graph one cycle of 1 sec x. Label the five points (high, low, endpoints, 3 and middle point). Give the amplitude, period, and phase shift Graph one cycle of 4cot x. Label the five points (high, low, endpoints, 8 4 and middle point). Give the amplitude, period, and phase shift. 14. Use addition or subtraction formulas to find the exact solution. 19 sin If 4 sin where is in QIII and 5 sin tan a) b) sec 4 where is in QII, find: 7
2 SOLUTIONS: 1. 53, a18.1, c 30.1 Area = , b 8.9, c 3. Area = , a 30.8, b 8.8 Area = k, k, k : EC,, k 4 40 : EC,, k 8 4 k , : EC,, & 8 are not given on this worksheet t 9. d 5sin a) The point starts units above the origin and moves downward, reaching the origin at t.39 seconds. It continues moving down with decreasing speed, reading the low point units below the x-axis at time t.79 seconds. The point then reverses direction, moving up and crossing the axis at time t 1.18 seconds before reaching to a point units above the x-axis at time t 1.57 seconds b) feet c) 1.57 f 0.64 oscillations per second feet 1. amp = 1 3, pd =, ph sh =, endpts = 5, 13. amp = 4, pd = 8, ph sh =, endpts =,6, increasing and or 8411
3 MATH 1113 Practice Test 6 SPRING 016 Find all solutions to the equation. EC for finding solutions on the interval 0,. 3 sin x 6 3. Find the exact value of the expression whenever it is defined. 1 8 csctan 4 Find the exact value of the expression whenever it is defined tan arccos sin cos arctan 6. 1 sec tan 5 Find all the solutions to the equations. For extra credit give the solutions on the interval 0,. Give the exact solution when appropriate. 7. cos 3t cos 5t sin 3t sin 5t 8. 1sin 3 cos 9. sin 6 3sin Find all the solutions to the equations. For extra credit give the solutions on the interval 0,360. 5sin 3 3sin Solve the triangle given that 3, c= 574, b = Solve the triangle given that a = 5, c = 6, and Solve the triangle given that a = 195, b = 48, and Solve the triangle given that a = 10, b = 15, and c = Solve the triangle given that b = 0, a = 10, and Solve the triangle given that c = 40, b = 70, and Solve the triangle given that c = 14, a = 87, and Alan is golfing and sets up for a long drive. He slices it, so it heads in a direction of 70 (forming an angle inside the triangle of 110 ) and hits a tree 80 feet away. The ball ricochets off the tree at a 0 angle (again inside the triangle) and comes to a stop.
4 Form a triangle with the 80 feet between the two angle measures. Find the distance his ball traveled by finding the length of the side across from the110. Round to one decimal place. 19. An airplane has to fly between three airports. The trip from the first to the second is 10 miles. After landing at the second airport, the plane must turn towards the third airport forming a 40 inside the triangle. At the third airport, the plane turns towards home forming an 80 inside the triangle. How far does the airplane have to travel to get home? Round to one decimal place. 0. Find the rectangular coordinates of the points given in polar form. 4, 3 1. The rectangular coordinates of a point are given. Find two pairs of polar coordinates r, for each point, one with r > 0 and the other with r < 0. Express in radians.,. Write the complex number in polar form. Express your argument in degrees. a) 9 3 9i b) 1 3i 3. Use the information found in problem to multiply the two complex numbers. Return your final answer to a bi form. Show work in polar form. 4. For the given z and w find z. Show your final answer to a + bi form. Show w z cos05 isin 05 w 3 cos85 i sin 85 work in polar form. a), 1 b) z 3cos10 isin10, w cos7 i sin 7 5. The vector v has initial point P and terminal point Q. Write v in the form ai + bj. P 3, ; Q 6,5 Find the dot product vwand the angle between v and w where v 3 i j, w i j 7. v i j, w i j 8. v 5i 1 j, w 6i j 9. v i j, w 3i j Decompose v into two vectors, one parallel to w and the other orthogonal to w. 30. v 3i j, w i j 31. v 4 i j, w i j 3. Find the fifth roots of 8 8i. 33. Write the expression in the standard a + bi form cos isin
5 SOLUTIONS: Must show work to receive credit n, n,,, k t ;,,,,,,, ,,,,,,,, n, n n,, n , n n,,,,,,, ,,,,,,,,,, n, n, n 7.9, 5.1, 90, 17.9, 17.1, , 14.1, a Area = 54, b1 b , 11.4, 7.4, 1.5, 53.4, 16.6 Area 1 = 14.9 and Area = No such triangle and no such area , 85.5, 5.9 Area = , 38.1, c 13.6 Area = , 33., a 69.7 Area = 1, , 9.4, b 84. Area = feet miles i 3 1. r 4, or r 4, 4 4. a) 18(cos150 isin150 ) b) (cos300 isin300 ) 3. 36(cos90 isin90 ) 36i 4. 3(cos6 isin 6 ) i 5. 9i 3j 6. vw, vw 5,
6 8. vw 6, vw 10, v1 i j, v i j 31. v 1 i j, v i j w0 cis i ; w1 cis i w cis i ; w3 cis.5 1.6i w4 cis i cis i
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