uiz 2 SHOW ALL WORK to receive credit. 1. 3 pts. Use the sum or difference identities to evaluate exactly (no decimal approximations): cos285 2. In questions 2A, 2B, 2C, and 2D below, find the exact values using the given information: sin = -5/12 with between and 3/2 cos = 2/5 with between 3/2 and 2 3 pts. 2A. Find sin( - ) 3 pts. 2B. Find tan(2) 3 pts. 2C. Find cos(/2) 2 pts. 2D. Find sec(/2 - ) Problems 3 to 5: 1 pt. each. Find the values exactly. 3. arccos (-1/2) 4. arcsin (-1) 5. arccot (3/3) 6. 2 pts. Find this value exactly: arccos [sin(11/6)] 7. 7 pts. For the function = 2cos[ + 4 (2 pts.) Graph at least one period of the function. (3 pts.) Find the amplitude, period, and phase shift. (2 pts.) Also find two different ordered pairs on the graph of the function, the first point when x is 0, and the second point when y is -2. The amplitude is __________ The period is ___________ The phase shift is ________ Two points on the graph are: (0, ____) and (___, -2). 8. 4 pts. Solve, finding all solutions in the interval Quiz 2 SHOW ALL WORK to receive credit. 1. 3 pts. Use the sum or difference identities to evaluate exactly (no decimal approximations): cos285 2. In questions 2A, 2B, 2C, and 2D below, find the exact values using the given information: sin = -5/13 with between and 3/2 cos = 2/5 with between 3/2 and 2 3 pts. 2A. Find sin( - ) 3 pts. 2B. Find tan(2) 3 pts. 2C. Find cos(/2) 2 pts. 2D. Find sec(/2 - ) Problems 3 to 5: 1 pt. each. Find the values exactly. 3. arccos (-1/2) 4. arcsin (-1) 5. arccot (3/3) 6. 2 pts. Find this value exactly: arccos [sin(11/6)] 7.7 pts. For the function = 2cos[1/6 + /4 ] (2 pts.) Graph at least one period of the function. (3 pts.) Find the amplitude, period, and phase shift. (2 pts.) Also find two different ordered pairs on the graph of the function, the first point when x is 0, and the second point when y is -2. The amplitude is __________ The period is ___________ The phase shift is ________ Two points on the graph are: (0, ____) and (___, -2). 8. 4 pts. Solve, finding all solutions in the interval MATH 108 Fall 2016 Quiz 1 Problem 1. 2 pts. Convert 108 to radian measure. Leave your answer in terms of . Problems 2 through 5. 1 pt. each. Find the exact value for each, if it exists. Finding an \"exact value\" means that decimal approximations from your calculator are not acceptable as answers. 2. cos(4/3) 3. sin(-300) 4. cot(3/2) 5. sec(135) Problem 6. 5 pts. Prove the identity. Use algebra and basic trigonometric formulas to transform one side of the equation to look like the other side. Show the whole process, without skipping any steps, and explain what you are doing in each step. Prove: sin2x tan2x = tan2x - sin2x Problem 7. 3 pts. Solve, using a calculator. A wheel with a 20 inch diameter is turning at the rate of 54 revolutions per minute. What is the linear speed of a point on the rim, measured to the nearest inch per minute? Problem 8. 5 pts. Find the exact values of the remaining 5 circular functions (sine, tangent, cotangent, secant, and cosecant) for angle , given that cos = 1/8 and is an angle in the 4th quadrant. Find exact answers for this problem- no credit for approximations. Reduce any fractions to lowest terms. Problem 9. 4 pts. Solve, finding ALL solutions. Express your answer exactly, and in radians. Solve sin = Problems 10-11. 2 pts. each. Use a calculator to find the function values to four decimal places. 10. csc125 11. tan(-5/9) Problem 12. 3 pts. Solve, using a calculator. From a spot marked X, the angle of elevation to the top of a cliff is 2924'. If the bottom of the cliff is 1850 feet from spot X, how high is the cliff (to the nearest foot)? Assume that a right triangle is formed. Top of clif 1850 feet X Bottom of cliff Fall 2016 MATH 108 Quiz 3 Show all work! No credit for answers without work shown. 1. 5 pts. Solve, finding all exact solutions in [0, 2). 4cos2x sinx + 4sin2x - 5sinx = 0 2. 5 pts. Solve, finding all solutions in [0, 360). Use a calculator to find all solutions to the nearest tenth of a degree. 2sec2x + secx = 3 3. 5 pts. Solve the triangle(s), if possible. Answers should be accurate to the nearest tenth of a degree. Side a = 30, side b = 22, side c =10 4. 5 pts. Solve the triangle(s), if possible. Answers should be accurate to the nearest hundredth. = 20.4 a = 18 (Side a is opposite angle .) b = 27 For problems 5 and 6, use the bearings described on page 905 of the College Trigonometry textbook. 5. 5 pts. Location A is 5 miles due south of Location B. The bearing of a fire from A is S41W and the bearing of the same fire from B is S29W. Find the distance from the fire to Location B to the nearest hundredth of a mile. (Drawing the diagram before you attempt the math can be very helpful.) 6. 5 pts. Two people leave from the same point at the same time. The first travels in a straight line N68E at 39 miles per hour and the second goes in a straight line S18W at 30 miles per hour. After 1 hour, how far apart are the people, to the nearest tenth of a mile? Fall 2016 MATH 108 Quiz 4 Problem 1. 2 pts. Convert the polar point (8, 3/4) into rectangular coordinates (x,y). Compute the coordinates exactly. Problem 2. 2 pts. Convert the rectangular point (-6, 0) into polar coordinates in the form (r, ). . Problem 3A. 6 pts. Fill in the blanks in the listed polar points (r, ) below, to satisfy the polar function r = 2 - 4 cos (/2) Given = -/3, find r: ( ____, -/3) Given = 0, find r: ( _____, 0) Given r = 0, find : ( 0, ____ ) (Note that there are an infinite number of correct answers for this and you only need to find one.) 4 pts. 3B. Graph the polar function r = 2 - 4 cos (/2) You can plot by hand, with an online grapher, or graphing calculator. Locate and mark the three points you found above on your graph. Problem 4. 10 pts. 2 pts. A. Vector has a magnitude of 20 and when drawn in standard position, makes an angle of 16 with the positive x axis. Draw vector and resolve it into its component form. Round your answers to the nearest hundredth. 2 pts. B. Vector has a magnitude of 14 and when drawn in standard position, makes an angle of 126 with the positive x axis. Draw vector and resolve it into its component form. Round your answers to the nearest hundredth. 1 pt. C. Draw the vector sum + in standard position. 2 pts. D. Find the component form of + . 1 pt. E. Find the magnitude of + 2 pts. F. Find the angle the vector sum + makes with the positive x axis. Problem 5. Vector is < -2, -8>. Vector is < 3, 2 > 2 pts. 5A. Find the dot product 4 pts. 5B. Find the angle between and . should be an angle between 0 and 180, rounded to the nearest hundredth. QUIZ Discussion Use the given information about to find the exact values of cos (/2) cos () = 3/5 where 0 /2 Select a different trigonometric function from the list below. Find the amplitude, period, and phase shift for your trigonometric function and post a graph of at least one period. y = cos (1/2 x + /2) +3 solve the equation, giving the exact solutions which lie in [0, 2] sin(x) + cos(x) = 1 Start by drawing a diagram of the situation in your selected word problem. Clearly label which direction is north, south, east, and west in your diagram, and label the known sides and angles in your triangle. Then use the Law of Cosines or Law of Sines to solve the problem. A vehicle travels due west for 30 miles. Then it turns and goes 30 miles in the direction of S68W. How far is it from the starting place? Find 2 ordered pairs of numbers in the polar form (r,) which satisfy your equation. Then find the points in Cartesian coordinates (x,y) that are equivalent to the two polar points you just found. Plug that angle in for in your equation, and compute the corresponding value of r. x = rcos and y = rsin Write your equivalent Cartesian coordinates points in form (x,y) CHECK: Do your polar points and their corresponding Cartesian coordinates land on the same point when graphed? r = 3cos Write your answer in the polar coordinates form (r, ) Repeat the steps above for another chosen value of . Use the conversion formulas for converting polar points to Cartesian coordinates. Pick a set of vectors u and v from the list below, and do the following 5 items: A. Draw each vector in standard position. QUIZ Discussion B. Find the magnitude of vector u: ||u|| C. Find the difference of vectors < u - v > D. Find the magnitude of vector < u - v > : || u - v || E. Find the angle , in degrees, between the vectors u and v. should be between 0 and 180 2. u = < 4, 5 > and v = < -1, -15 > Determine if the given equation is a parabola, ellipse, circle, or hyperbola. If it is a parabola find the vertex point, focus, directrix, and determine which way it will open (up, down, right, or left). If it is an ellipse, find the center point and vertices, and determine if it is short and wide or tall and thin. If it is a circle, find the center and radius. If it is a hyperbola, find the center point and vertices, and determine which way it will open (up and down, or right and left). (y+2)2 = 4(x+6) MATH 108 Fall 2016 Quiz 1 Problem 1. 2 pts. Convert 108 to radian measure. Leave your answer in terms of . Problems 2 through 5. 1 pt. each. Find the exact value for each, if it exists. Finding an \"exact value\" means that decimal approximations from your calculator are not acceptable as answers. 2. cos(4/3) 3. sin(-300) 4. cot(3/2) 5. sec(135) Problem 6. 5 pts. Prove the identity. Use algebra and basic trigonometric formulas to transform one side of the equation to look like the other side. Show the whole process, without skipping any steps, and explain what you are doing in each step. Prove: sin2x tan2x = tan2x - sin2x Problem 7. 3 pts. Solve, using a calculator. A wheel with a 20 inch diameter is turning at the rate of 54 revolutions per minute. What is the linear speed of a point on the rim, measured to the nearest inch per minute? Problem 8. 5 pts. Find the exact values of the remaining 5 circular functions (sine, tangent, cotangent, secant, and cosecant) for angle , given that cos = 1/8 and is an angle in the 4th quadrant. Find exact answers for this problem- no credit for approximations. Reduce any fractions to lowest terms. Problem 9. 4 pts. Solve, finding ALL solutions. Express your answer exactly, and in radians. Solve sin = Problems 10-11. 2 pts. each. Use a calculator to find the function values to four decimal places. 10. csc125 11. tan(-5/9) Problem 12. 3 pts. Solve, using a calculator. From a spot marked X, the angle of elevation to the top of a cliff is 2924'. If the bottom of the cliff is 1850 feet from spot X, how high is the cliff (to the nearest foot)? Assume that a right triangle is formed. Top of clif 1850 feet X Bottom of cliff Fall 2016 MATH 108 Quiz 3 Show all work! No credit for answers without work shown. 1. 5 pts. Solve, finding all exact solutions in [0, 2). 4cos2x sinx + 4sin2x - 5sinx = 0 2. 5 pts. Solve, finding all solutions in [0, 360). Use a calculator to find all solutions to the nearest tenth of a degree. 2sec2x + secx = 3 3. 5 pts. Solve the triangle(s), if possible. Answers should be accurate to the nearest tenth of a degree. Side a = 30, side b = 22, side c =10 4. 5 pts. Solve the triangle(s), if possible. Answers should be accurate to the nearest hundredth. = 20.4 a = 18 (Side a is opposite angle .) b = 27 For problems 5 and 6, use the bearings described on page 905 of the College Trigonometry textbook. 5. 5 pts. Location A is 5 miles due south of Location B. The bearing of a fire from A is S41W and the bearing of the same fire from B is S29W. Find the distance from the fire to Location B to the nearest hundredth of a mile. (Drawing the diagram before you attempt the math can be very helpful.) 6. 5 pts. Two people leave from the same point at the same time. The first travels in a straight line N68E at 39 miles per hour and the second goes in a straight line S18W at 30 miles per hour. After 1 hour, how far apart are the people, to the nearest tenth of a mile? Fall 2016 MATH 108 Quiz 4 Problem 1. 2 pts. Convert the polar point (8, 3/4) into rectangular coordinates (x,y). Compute the coordinates exactly. Problem 2. 2 pts. Convert the rectangular point (-6, 0) into polar coordinates in the form (r, ). . Problem 3A. 6 pts. Fill in the blanks in the listed polar points (r, ) below, to satisfy the polar function r = 2 - 4 cos (/2) Given = -/3, find r: ( ____, -/3) Given = 0, find r: ( _____, 0) Given r = 0, find : ( 0, ____ ) (Note that there are an infinite number of correct answers for this and you only need to find one.) 4 pts. 3B. Graph the polar function r = 2 - 4 cos (/2) You can plot by hand, with an online grapher, or graphing calculator. Locate and mark the three points you found above on your graph. Problem 4. 10 pts. 2 pts. A. Vector has a magnitude of 20 and when drawn in standard position, makes an angle of 16 with the positive x axis. Draw vector and resolve it into its component form. Round your answers to the nearest hundredth. 2 pts. B. Vector has a magnitude of 14 and when drawn in standard position, makes an angle of 126 with the positive x axis. Draw vector and resolve it into its component form. Round your answers to the nearest hundredth. 1 pt. C. Draw the vector sum + in standard position. 2 pts. D. Find the component form of + . 1 pt. E. Find the magnitude of + 2 pts. F. Find the angle the vector sum + makes with the positive x axis. Problem 5. Vector is < -2, -8>. Vector is < 3, 2 > 2 pts. 5A. Find the dot product 4 pts. 5B. Find the angle between and . should be an angle between 0 and 180, rounded to the nearest hundredth. QUIZ Discussion Use the given information about to find the exact values of cos (/2) cos () = 3/5 where 0 /2 Select a different trigonometric function from the list below. Find the amplitude, period, and phase shift for your trigonometric function and post a graph of at least one period. y = cos (1/2 x + /2) +3 solve the equation, giving the exact solutions which lie in [0, 2] sin(x) + cos(x) = 1 Start by drawing a diagram of the situation in your selected word problem. Clearly label which direction is north, south, east, and west in your diagram, and label the known sides and angles in your triangle. Then use the Law of Cosines or Law of Sines to solve the problem. A vehicle travels due west for 30 miles. Then it turns and goes 30 miles in the direction of S68W. How far is it from the starting place? Find 2 ordered pairs of numbers in the polar form (r,) which satisfy your equation. Then find the points in Cartesian coordinates (x,y) that are equivalent to the two polar points you just found. Plug that angle in for in your equation, and compute the corresponding value of r. x = rcos and y = rsin Write your equivalent Cartesian coordinates points in form (x,y) CHECK: Do your polar points and their corresponding Cartesian coordinates land on the same point when graphed? r = 3cos Write your answer in the polar coordinates form (r, ) Repeat the steps above for another chosen value of . Use the conversion formulas for converting polar points to Cartesian coordinates. Pick a set of vectors u and v from the list below, and do the following 5 items: A. Draw each vector in standard position. QUIZ Discussion B. Find the magnitude of vector u: ||u|| C. Find the difference of vectors < u - v > D. Find the magnitude of vector < u - v > : || u - v || E. Find the angle , in degrees, between the vectors u and v. should be between 0 and 180 2. u = < 4, 5 > and v = < -1, -15 > Determine if the given equation is a parabola, ellipse, circle, or hyperbola. If it is a parabola find the vertex point, focus, directrix, and determine which way it will open (up, down, right, or left). If it is an ellipse, find the center point and vertices, and determine if it is short and wide or tall and thin. If it is a circle, find the center and radius. If it is a hyperbola, find the center point and vertices, and determine which way it will open (up and down, or right and left). (y+2)2 = 4(x+6)