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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

In Exercises sketch the curves of the given trigonometric functions. Check each using a calculator.y = 2/3 sinx
Sketch the graph of y = 2 sin x + cos 2x by addition of ordinates.
In Exercises sketch the curves of the given functions by addition of ordinates.y = sin x + cos x
In Exercises, determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator. y = 2 cos(x - k|00 )
Complete the following table for the given functions and then plot the resulting graphs.y = −4 sin x X y X y 一于 +4 平 - 27. 2 4 3吋 π
Fill in the following table for each function and plot the graph from these points.y = csc x k EIN ابا KIT 0 KIT 1 X
Complete the following table for the given functions and then plot the resulting graphs.y = −3 cos x X y X y 一于 +4 平 - 27. 2 4 3吋 π
If the period is 1/5s find ω.
In Exercises find the amplitude and period of each function and then sketch its graph.y = 28 cos 10x
Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator. M (2 y = cos(x +. (9
Determine each of the following as being either true or false. If it is false, explain why. The graph of y = sin x− 2 cos 1/2x passes through (π, 0).
A wave is traveling in a string. The displacement y (in in.) as a function of the time t (in s) from its equilibrium position is given by y = A cos(2π/T)t. T is the period (in s) of the motion. If A
Sketch the curves of the given functions by addition of ordinates.y = 1/4x2 + cos3x
Fill in the following table for each function and plot the graph from these points.y = sec x k EIN ابا KIT 0 KIT 1 X
If ω = 40π rad/s, find the period.
Find the amplitude and period of each function and then sketch its graph.y = 3 cos 8x
Complete the following table for the given functions and then plot the resulting graphs.y = cos x X y X y 一于 +4 平 - 27. 2 4 3吋 π
Fill in the following table for each function and plot the graph from these points.y = cot x k EIN ابا KIT 0 KIT 1 X
Determine each of the following as being either true or false. If it is false, explain why. The frequency of an alternating current described by the equation i = 8 sin 60πt (t in s) is 120 Hz.
Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator. y = 3 sin(x + 7 4
Complete the following table for the given functions and then plot the resulting graphs.y = sin x X y X y 一于 +4 平 - 27. 2 4 3吋 π
Sketch the graphs of the given functions.y = 2 sin(2x − π/3)
Sketch the curves of the given functions by addition of ordinates.y = 1/10x2 − sinπx
If the period is 1/10s, find f.
Find the amplitude and period of each function and then sketch its graph.y = 4 sin 2x
Determine the amplitude, period, and displacement for each function. Then sketch the graphs of the functions. Check each using a calculator. sin(x - 2) y sin
Sketch the graphs of the given functions.y = 3 sec x
Determine each of the following as being either true or false. If it is false, explain why.The displacement of the graph of y = -2 cos (2x)is-. 4 8
Sketch the curves of the given functions by addition of ordinates.y = x − sin x
Fill in the following table for each function and plot the graph from these points.y = tan x k EIN ابا KIT 0 KIT 1 X
If f = 40 cycles min, find the period.
Graph the function if the given changes are made in the indicated examples of this section.In Example 3, if the coefficient of x is changed from 3 to 4, sketch the graph of the resulting
Find the amplitude and period of each function and then sketch its graph.y = 2 sin 6x
In Exercises, graph the function if the given changes are made in the indicated examples of this section.In Example 4, if the sign before π/6 is changed, sketch the graph of the resulting
In Exercises answer the given questions about the indicated examples of this section.In Example 2, if the blade starts at an angle of −45°, what is the equation relating d and t as (a) A sine
Sketch the graphs of the given functions.y = 2 + 3sin x
Graph the function if the given changes are made in the indicated examples of this section.In Example 2, if the sign of the coefficient of cos x is changed, plot the graph of the resulting
Sketch the curves of the given functions by addition of ordinates.y = 1/3x + sin2x
In Exercises, view the graphs on a calculator if the given changes are made in the indicated examples of this section.In Example 3, change the sign before π/4.Data from Example 3View at least two
In Exercises answer the given questions about the indicated examples of this section.In Example 1, what is the equation relating d and t if the end of the radius starts at (0, R)?Data from Example
Determine each of the following as being either true or false. If it is false, explain why.The period of the graph of y = 4 sin 1/2πx is 4.
In Exercises, graph the function if the given changes are made in the indicated examples of this section.In Example 3, if the sign before π/6 is changed, sketch the graph of the resulting
In Exercises, view the graphs on a calculator if the given changes are made in the indicated examples of this section.In Example 2, change 0.5 to 5.Data from Example 2View at least two cycles of the
Graph the function if the given changes are made in the indicated examples of this section.In Example 2, if the coefficient of x is changed from 4 to 6, graph one complete cycle of the resulting
In Problems sketch the graphs of the given functions.y = 0.5 cos π/2x
In Exercises sketch the curves of the given functions by addition of ordinates.y = 3 − 2 cos x
Determine each of the following as being either true or false. If it is false, explain why.A point on the graph of y = 2 cos x is (π, −2).
A sailboat is headed due north, and its sail is set perpendicular to the wind, which is from the south of west. The component of the force of the wind in the direction of the heading is 480 N, and
Determine the amplitude, period, and displacement of the function y = −3 sin(4πx − π/3).
In Exercises sketch the curves of the given functions by addition of ordinates.y = 1 + sin x
The resultant of three horizontal forces, 45 N, 35 N, and 25 N, that act on a bolt is zero. Write a paragraph or two explaining how to find the angles between the forces.
Boston is 650 km and 21.0° south of west from Halifax, Nova Scotia. Radio signals locate a ship 10.5° east of south from Halifax and 5.6° north of east from Boston. How far is the ship from each
A plane is traveling horizontally at 1250 ft/s. A missile is fired horizontally from it 30.0° from the direction in which the plane is traveling. If the missile leaves the plane at 2040 ft/s, what
One end of a 1450-ft bridge is sighted from a distance of 3250 ft. The angle between the lines of sight of the ends of the bridge is 25.2°. From these data, how far is the observer from the other
In going around a storm, a plane flies 125 mi south, then 140 mi at 30.0° south of west, and finally 225 mi at 15.0° north of west. What is the displacement of the plane from its original position?
Find the side x in the truss in Fig. 9.90.Fig. 9.90. 3.30 ft 2.31 ft 1.82 ft X 2.02 ft
Atlanta is 290 mi and 51.0° south of east from Nashville. The pilot of an airplane due north of Atlanta radios Nashville and finds the plane is on a line 10.5° south of east from Nashville. How far
A surveyor wishes to find the distance between two points between which there is a security-restricted area. The surveyor measures the distance from each of these points to a third point and finds
The angle of depression of a fire noticed west of a fire tower is 6.2°. The angle of depression of a pond, also west of the tower, is 13.5°. If the fire and pond are at the same altitude, and the
A water skier is towed 65 m to the south of the starting point, and then is turned 40° east of south for another 35 m. What is the skier’s displacement from the starting point?
The GPS of a plane over Lake Erie indicates that the plane’s position is 190 km from Detroit and 110 km from London, Ontario, which are known to be 160 km apart. What is the angle between the
Solve the triangles with the given parts.b = 750, c = 1100, A = 56°
Find the required horizontal and vertical components of the given vectors. A car is being unloaded from a ship. It is supported by a cable from a crane and guided into position by a horizontal rope.
In an automobile safety test, a shoulder and seat belt exerts a force of 95.0 lb directly backward and a force of 83.0 lb backward at an angle of 20.0° below the horizontal on a dummy. If the belt
Three pipes of radii 2.50 cm, 3.25 cm, and 4.25 cm are welded together lengthwise. See Fig. 9.89. Find the angles between the center-to-center lines. Fig. 9.89 1
In Fig. 9.88, a damper mechanism in an air-conditioning system is shown. If θ = 27.5° when the spring is at its shortest and longest lengths, what are these lengths? ស 2.70 m Fig. 9.88 1.25 m
A crate weighing 562 lb hangs from two ropes which are angled 41.5° and 37.2° from the vertical as shown in Fig. 9.87. Make a free body diagram, and then find the tensions TL and TR in the
Two satellites are being observed at the same observing station. One is 22,500 mi from the station, and the other is 18,700 mi away. The angle between their lines of observation is 105.4°. How far
A water molecule (H2O) consists of two hydrogen atoms and one oxygen atom. The distance from the nucleus of each hydrogen atom to the nucleus of the oxygen atom is 0.96 pm and the bond angle (see
In order to get around an obstruction, an oil pipeline is constructed in two straight sections, one 3.756 km long and the other 4.675 km long, with an angle of 168.85° between the sections where
A boat is tied to a dock at two points using ropes as shown in Fig. 9.85. The boat exerts a force of 325 N at an angle of 25° from the line perpendicular to the dock. Make a free-body diagram, and
A bullet is fired from the ground of a level field at an angle of 39.0° above the horizontal. It travels in a straight line at 2200 ft/s for 0.20 s when it strikes a target. The sound of the strike
In Fig. 9.84, F represents the total surface tension force around the circumference on the liquid in the capillary tube. The vertical component of F holds up the liquid in the tube above the liquid
Three forces of 3200 lb, 1300 lb, and 2100 lb act on a bolt as shown in Fig. 9.83. Find the resultant force. 1300 lb 54° 35° Fig. 9.83 2100 lb 32% 3200 lb
A magnetic force of 0.15 N is applied at an angle of 22.5° above the horizontal on an iron bar. A second magnetic force of 0.20 N is applied from the opposite side at an angle of 15.0° above the
A shearing pin is designed to break and disengage gears before damage is done to a machine. In a test, a vertically upward force of 8250 lb and a 7520 lb at 35.0° below the horizontal are applied to
Assuming the vectors in Fig. 9.82 are in equilibrium, find T1 and T2. Fig. 9.82 427 lb 72.5° T₂ T₁ 22.6°
A helium-filled balloon rises vertically at 3.5 m/s as the wind carries it horizontally at 5.0 m/s. What is the resultant velocity of the balloon?
Find the horizontal and vertical components of the velocity shown in Fig. 9.81. 307.44° y 0 170.5 km/h Fig. 9.81
Solve the given problems. Use a ruler and protractor as in Examples 6 and 7. While unloading a crate weighing 610 N, the chain from a crane supports it with a force of 650 N at an angle of 20° from
Solve the given problems. Use a ruler and protractor as in Examples 6 and 7. A ship travels 20 km in a direction of 30° south of east, then turns and goes due south for another 40 km, and finally
Find the horizontal and vertical components of the force shown in Fig. 9.80. 175.6 lb y 152.48° 0 Fig. 9.80
A rocket is launched at an angle of 42.0° with the horizontal and with a speed of 2500 ft/s. What are its horizontal and vertical components of velocity?
Solve the given problems. Use a ruler and protractor as in Examples 6 and 7. A rope holds a helium-filled balloon in place with a tension of 510 N at an angle of 80° with the ground due to a wind.
Solve the given problems. Use a ruler and protractor as in Examples 6 and 7. A driver takes the wrong road at an intersection and travels 4 mi north, then 6 mi east, and finally 10 mi to the
A storm cloud is moving at 15 mi/h from the northwest. A television tower is 60° south of east of the cloud. What is the component of the cloud’s velocity toward the tower?
In a ballistics test, a bullet was fired into a block of wood with a velocity of 2200 ft/s and at an angle of 71.3° with the surface of the block. What was the component of the velocity
Solve the given problems. Use a ruler and protractor as in Examples 6 and 7. A ski tow is moving skiers vertically upward at 24 m/min and horizontally at 44 m/min. What is the velocity of the
Solve the given problems. Use a ruler and protractor as in Examples 6 and 7. A jet travels 17 km in a straight line as it also descends 8 km. It then turns upward and travels 10 km in a straight line
Solve the given problems. Use a ruler and protractor as in Examples 6 and 7. Two electric charges create an electric field intensity, a vector quantity, at a given point. The field intensity is 30
An architect determines the two acute angles and one of the legs of a right triangular wall panel. Show that the area At is A₁ a² sin B 2 sin A
Two forces that act on an airplane wing are called the lift and the drag. Find the resultant of these forces acting on the airplane wing in Fig. 9.10.Data from Example 6Two persons pull horizontally
If A = 30° and b = 18, what values of a will result in the ambiguous case with two triangle solutions? Explain.
Find the indicated vector sums and differences with the given vectors by means of diagrams.D − 2C − 1/2E A B C D E
A triangular brace is designed such that sides meet at angles of 42.0° and 59.5°, with the longest side being 5.00 cm longer than the shortest side. What is the perimeter of the brace?
Three straight streets intersect each other such that two of the angles of intersection are 22° and 112°, and the shortest distances between any two intersections is 540 m. What is the longest
A traffic light that weighs 215 N is suspended from two cables which are angled 30.0° and 53.0° from the vertical as shown in Fig. 9.50. Make a free-body diagram, and then find the tensions TL and
Find the indicated vector sums and differences with the given vectors by means of diagrams.C − B − 3/4A A B C D E
Solve the triangles with the given parts.a = 47.4, b = 40.0, c = 45.5
A triangular machine part has sides of 5 cm and 8 cm. Explain why the law of sines, or the law of cosines, is used to start the solution of the triangle if the third known part is (a) The third

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