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mathematics
algebra and trigonometry graphs

Questions and Answers of Algebra And Trigonometry Graphs

Find two real numbers between -2π and 2π that determine each of the points on the unit circle. M D Y^ N H x
For angles of the following measures, state in which quadrant the terminal side lies. It helps to sketch the angle in standard position.-460.5°
Find the function value using coordinates of points on the unit circle. Give exact answers.sin π
Find two positive angles and two negative angles that are coterminal with the given angle.214°30′
Determine the amplitude, the period, and the phase shift of the function and, without a graphing calculator, sketch the graph of the function by hand. Then check the graph using a graphing
For angles of the following measures, state in which quadrant the terminal side lies. It helps to sketch the angle in standard position.1075°
Find two real numbers between -2π and 2π that determine each of the points on the unit circle. M P ул N 1 X
In Exercises, find the six trigonometric function values of the specified angle. 8.2
Find two positive angles and two negative angles that are coterminal with the given angle.-75°
A number b determines a point on the unit circle with coordinates ( -2/3, √5/3). What are the coordinates of the point determined by -β?
For angles of the following measures, state in which quadrant the terminal side lies. It helps to sketch the angle in standard position.800°
In Exercises, find the six trigonometric function values of the specified angle.
The number π/4 determines a point on the unit circle with coordinates (√2/2, √2/2). What are the coordinates of the point determined by -π/4?
The following points are on the unit circle. Find the coordinates of their reflections across (a) The x-axis, (b) The y-axis, and (c) The origin. √3 (-1/³--1) 2 2
Find the exact function value, if it exists.cos 3π
Determine the amplitude, the period, and the phase shift of the function and, without a graphing calculator, sketch the graph of the function by hand. Then check the graph using a graphing
For each of Exercises, sketch a unit circle and mark the points determined by the given real numbers.a) -π/2b) -3π/4c) -5π/6d) -5π/2e) -17π/2f) -9π/4
For angles of the following measures, state in which quadrant the terminal side lies. It helps to sketch the angle in standard position.-120°
In Exercises, find the six trigonometric function values of the specified angle. 6 13
Determine the amplitude, the period, and the phase shift of the function and, without a graphing calculator, sketch the graph of the function by hand. Then check the graph using a graphing
The following points are on the unit circle. Find the coordinates of their reflections across (a) The x-axis, (b) The y-axis, and (c) The origin. 2 5' V21 5
Find the exact function value, if it exists.tan ( -45°)
Determine the amplitude, the period, and the phase shift of the function and, without a graphing calculator, sketch the graph of the function by hand. Then check the graph using a graphing
For each of Exercises, sketch a unit circle and mark the points determined by the given real numbers.a) π/6b) 2π/3c) 7π/6d) 10π/6e) 14π/4f) 23π/4
For angles of the following measures, state in which quadrant the terminal side lies. It helps to sketch the angle in standard position.245°15′
Find the six trigonometric function values of θ. 4 V65 7 Ө
In Exercises, find the six trigonometric function values of the specified angle. 3 at 6 3V3
The following points are on the unit circle. Find the coordinates of their reflections across (a) The x-axis, (b) The y-axis, and (c) The origin. 2 V5 3 3
Find the exact function value, if it exists.sin 120°
For each of Exercises, sketch a unit circle and mark the points determined by the given real numbers.a) π/2b) 5π/4c) 2πd) 9π/4e) 13π/4f) 23π/4
For angles of the following measures, state in which quadrant the terminal side lies. It helps to sketch the angle in standard position.-14.3°
In Exercises, find the six trigonometric function values of the specified angle. 0.3 0.4 0.5 B
Determine the amplitude, the period, and the phase shift of the function and, without a graphing calculator, sketch the graph of the function by hand. Then check the graph using a graphing
For each of Exercises, sketch a unit circle and mark the points determined by the given real numbers.a) π/4b) 3π/2c) 3π/4d) πe) 11π/4f) 17π/4
The following points are on the unit circle. Find the coordinates of their reflections across (a) The x-axis, (b) The y-axis, and (c) The origin. 3 4' 4 7
For angles of the following measures, state in which quadrant the terminal side lies. It helps to sketch the angle in standard position.187°
In Exercises, find the six trigonometric function values of the specified angle. 15 8 17
Liposuction and nose reshaping are two of the five most popular cosmetic surgeries in the United States. Together, these two procedures accounted for 427,676 surgeries in 2014. The number of
Graph.y > 2x
Computerwarehouse.com charges $8 to ship orders up to 10 lb, $12 for orders from 10 lb up to 15 lb, and $15 for orders of 15 lb or more. One day, shipping charges for 150 orders totaled $1620. The
Graph.2y < x
Graph.y + x ≥ 0
Graph.y - x < 0
Graph.y > x - 3
Graph.y ≤ x + 4
Find the maximum value and the minimum value of Q = 2x + 3y subject to x + y ≤ 6, 2х - 3y ≥ -3, x 2 1, y = 0. ≥
Graph.x - y ≥ 5
Graph.x + y < 4
At the 2014 Paralympic Games in Sochi, Russia, the top three countries—the Russian Federation, Ukraine, and the United States—won a total of 123 medals. Ukraine won 7 more medals than the United
Graph.3x - 2y ≤ 6
Graph.2x - 6y ≥ 8 + 2y
Graph.2x - 5y ≤ 10
Graph.3y + 2x ≥ 6
Graph.2y + x ≤ 4
Graph.3x - 2 ≤ 5x + y
Graph.x < -4
Graph.y > -3
Graph.y ≥ 5
Graph.x ≤ 5
The value of 75 coins, consisting of only nickels and dimes, is $5.95. How many of each kind of coin are there?
Graph.-4 < y < -1
The Davidson family invested $5000, part at 3% and the remainder at 3.5%. The annual income from both investments is $167. What is the amount invested at each rate?
Graph.-3 ≤ x ≤ 3
The produce manager at Stan’s Market orders 40 lb of tomatoes, 20 lb of zucchini, and 30 lb of onions from a local farmer one week.a) Write a 1 * 3 matrix A that represents the amount of each item
A dietician must plan a breakfast menu that provides 460 Cal, 9 g of fat, and 55 mg of calcium. One plain bagel contains 200 Cal, 2 g of fat, and 29 mg of calcium. A one-tablespoon serving of cream
Graph.y ≥ | x|
Graph.y ≤ |x + 2|
Use Gaussian elimination or Gauss–Jordan elimination in Exercises.Greenfield Manufacturing borrowed $30,000 to buy a new piece of equipment. Part of the money was borrowed at 8%, part at 10%, and
During the holiday season, Brianna sold scarves at a kiosk in a shopping mall. Embroidered floral scarves cost $24 each, and sheer chevron scarves cost $18 each. One day she sold 39 scarves. Total
Use Gaussian elimination or Gauss–Jordan elimination in Exercises.One year, a family spent a total of $2500 on summer sports camps for their three sons. The amount spent on camps for the oldest son
Graph.y ≤ 3x + 6
Graph.4x - 3y ≥ 12
Which of the following is not a row-equivalent operation on a matrix?A. Interchange any two columns.B. Interchange any two rows.C. Add two rows.D. Multiply each entry in a row by -3.
In 2012, the annual mean wage of a paramedic in the state of Washington was $50,980. This wage was $8600 less than twice the annual mean wage of a paramedic in Kentucky. Find the annual median wage
In 2014, the number of international adoptions in the United States was at its lowest level since 2004. The number of international adoptions in 2014 totaled 6441, a decrease of 71.9% from 2004. Find
Consider the function f(x) = x2 - 4x + 3 in Exercises.What are the inputs if the output is 15?
Consider the function f(x) = x2 - 4x + 3 in Exercises.Given an output of 8, find the corresponding inputs.
Consider the function f(x) = x2 - 4x + 3 in Exercises.What is the output if the input is -9?
Consider the function f(x) = x2 - 4x + 3 in Exercises.Find the zeros of the function.
The Jeep Renegade Sport 4 * 4 vehicle gets 23 miles per gallon (mpg) in city driving and 32 mpg in highway driving. The car is driven 403 mi on 14 gal of gasoline. How many miles were driven in the
Comfort-by-Design Furniture produces chairs and sofas. Each chair requires 20 ft of wood, 1 lb of foam rubber, and 2 yd2 of fabric. Each sofa requires 100 ft of wood, 50 lb of foam rubber, and
Three gears are arranged as shown in the following figure. Find the angle ϕ. r = 28 ft 41° r = 22 ft r = 36 ft
A block weighing 100 lb rests on a 25° incline. Find the magnitude of the components of the block’s weight perpendicular to and parallel to the incline. 25°- а 100 25°/
Sketch (include the unit circle) and calculate the unit vector u = (cos u)i + (sin u)j for the given direction angle. Ꮎ 47 3
Multiply or divide and leave the answer in trigonometric notation. 8(cos 20° + i sin 20°) 2 (cos 25° + i sin 25°)
Sanchez Irrigation is installing a lawn irrigation system with three heads. They determine that the best locations for the heads A, B, and C are such that ∠CAB is 40° and ∠ACB is 45° and that
A hot-air balloon is rising vertically 10 ft/sec while the wind is blowing horizontally 5 ft/sec. Find the speed v of the balloon and the angle θ that it makes with the horizontal. 0 V 5
Find standard notation. 4[cos (327) + sin ( 377)] + i 2
Multiply or divide and leave the answer in trigonometric notation. TT 3( cos i sin): [(cos - + COS 3 3 TT 4 + i sin :)] 4
Find standard notation, a + bi. Vs(cos TT 8 cos + i sin 4 ㅠ 4
A boat heads 35°, propelled by a force of 750 lb. A wind from 320° exerts a force of 150 lb on the boat. How large is the resultant force F, and in what direction is the boat moving?
A zoo is expanding its African elephant exhibit and needs to fence an outdoor triangular area, with a barn forming one side of the triangle. The maintenance department has only 168 ft of fencing in
A pole leans away from the sun at an angle of 7° to the vertical. When the angle of elevation of the sun is 51°, the pole casts a shadow 47 ft long on level ground. How long is the pole?
Find standard notation, a + bi.10(cos 270° + i sin 270°)
Convert to trigonometric notation and then multiply or divide. (1 - i)(√3 - i)
The vectors u, v, and w are drawn below. Copy them on a sheet of paper. Then sketch each of the vectors in Exercises.u + v V W u
A new homeowner has a triangular- shaped back yard. Two of the three sides measure 53 ft and 42 ft and form an included angle of 135°. To determine the amount of fertilizer and grass seed to be
In Exercises, keep in mind the two types of bearing considered in Sections 6.2 and 6.3.A reconnaissance airplane leaves its airport on the east coast of the United States and flies in a direction of
A ship first sails N80°E for 120 nautical mi, and then S20°W for 200 nautical mi. How far is the ship, then, from the starting point and in what direction?
Convert to trigonometric notation and then multiply or divide. V3i 1 1 + i

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