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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.cotθ = 0.1519Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
Some of the streets of San Francisco are shown in Fig. 4.62. The distances between intersections A and B, A and D, and C and E are shown. How far is it between intersections C and D? B. C Golden Gate
Draw angles in standard position such that the terminal side passes through the given point.(−3, 8)
Find the values of the trigonometric functions. Round off results.(sec 79.36°)(sin 79.36°) − tan 79.36°
For an acute angle A > 45°, which is less, tan A or cot A?
A supporting girder structure is shown in Fig. 4.63. Find the length x. 7.25 m 39.4° 27.8° -x- Fig. 4.63 5.25 m
Find the indicated part of the right triangle that has the given parts.The hypotenuse is 964, and one angle is 17.6° . Find the longer leg
Draw angles in standard position such that the terminal side passes through the given point.(−3,−5)
Find a formula for the area of the trapezoidal aqueduct cross section shown in Fig. 4.64. Fig. 4.64 a b 0
Use a protractor to draw the given angle. Measure off 10 units (centimeters are convenient) along the radius vector. Then measure the corresponding values of x and y. From these values, determine the
Find θ for each of the given trigonometric functions. Assume θ is an acute angle. Round off results.cosθ = 0.850
If tan θ = 3/4, what is the value of sin2θ = cos2θ [sin2θ = (sinθ)2]
Find the indicated part of the right triangle that has the given parts.The legs are 0.596 and 0.842. Find the larger acute angle.
Draw angles in standard position such that the terminal side passes through the given point.(6,−1)
Use a protractor to draw the given angle. Measure off 10 units (centimeters are convenient) along the radius vector. Then measure the corresponding values of x and y. From these values, determine the
Find θ for each of the given trigonometric functions. Assume θ is an acute angle. Round off results.sinθ = 0.63052
If sinθ = 2/3, what is the value of sec2θ − tan2θ?
Find the exact area of a circle inscribed in a regular hexagon (the circle is tangent to each of the six sides) of perimeter 72.
Draw angles in standard position such that the terminal side passes through the given point.(−7, 5)
Use a protractor to draw the given angle. Measure off 10 units (centimeters are convenient) along the radius vector. Then measure the corresponding values of x and y. From these values, determine the
Find θ for each of the given trigonometric functions. Assume θ is an acute angle. Round off results.tanθ = 1.574
If y = sin θ, what is cos θ in terms of y?
Use a calculator to verify the given relationships or statements. [sin2θ = (sinθ)2] sin 43.7° cos 43.7° tan 43.7°
The diameter d of a pipe can be determined by noting the distance x on the V-gauge shown in Fig. 4.66. Points A and B indicate where the pipe touches the gauge, and x equals either AV or VB. Find a
Find the exact perimeter of an equilateral triangle that is inscribed in a circle (each vertex is on the circle) of circumference 20π.
Draw angles in standard position such that the terminal side passes through the given point.(−4,−2)
Use a protractor to draw the given angle. Measure off 10 units (centimeters are convenient) along the radius vector. Then measure the corresponding values of x and y. From these values, determine the
Find θ for each of the given trigonometric functions. Assume θ is an acute angle. Round off results.cosθ = 0.0135
If x = cosθ, what is tanθ in terms of x?
One World Trade Center refers to the main building of the rebuilt World Trade Center in New York City, which was opened in 2014. A person standing on level ground 350.0 ft from the base of the
Draw angles in standard position such that the terminal side passes through the given point.(−2, 0)
Find θ for each of the given trigonometric functions. Assume θ is an acute angle. Round off results.cscθ = 4.713
From the definitions of the trigonometric functions, it can be seen that cscθ is the reciprocal of sinθ. What function is the reciprocal of cosθ?
A communications satellite is in orbit 35,300 km directly above the Earth’s equator. What is the greatest latitude from which a signal can travel from the Earth’s surface to the satellite in a
The screen on a certain Samsung Galaxy tablet has 2048 pixels along its length and 1536 pixels along its width. Using a right triangle, find the angle between the longer side and the diagonal of the
Draw angles in standard position such that the terminal side passes through the given point.(0, 6)
In order to determine the length of a lake, a surveyor places poles in the ground at points A, B, and C and makes the measurements shown in Fig. 4.49. Determine the length of the lake, DE. A 28.74
Solve the right triangles with the given parts or state that there is not enough information to solve. Round off results according to Table 4.1. Refer to Fig. 4.37.a = 932, c = 1240Data from Table
Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points, give answers in exact form.(1.2, 0.9)
Find the values of the trigonometric functions. Round off results according to Table 4.1.sin 88°Data from Table 4.1 Angles and Accuracy of Trigonometric Functions Measurements of Angle to
Solve the right triangles with the given parts or state that there is not enough information to solve. Round off results according to Table 4.1. Refer to Fig. 4.37.B = 32.1°, c = 238Data from Table
Determine one positive and one negative coterminal angle for each angle given.−150°
Find the values of the trigonometric functions. Round off results according to Table 4.1.cos 0.7°Data from Table 4.1 Angles and Accuracy of Trigonometric Functions Measurements of Angle to
If tanθ = 9 40, find values of sinθ and cosθ. Then evaluate sinθ/cosθ (assume θ is acute).
Express the given angles in decimal form.31°54´
Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points, give answers in exact form.(1, √15)
The bottom of the doorway to a building is 2.65 ft above the ground, and a ramp to the door for the disabled is at an angle of 6.0° with the ground. How much longer must the ramp be in order to make
Determine one positive and one negative coterminal angle for each angle given.462°
In finding the wavelength λ (the Greek letter lambda) of light, the equation λ = d sinθ is used. Find λ if d = 30.05 μm and θ = 1.167°. (μ is the prefix for 10−6.)
Find θ if cosθ = 0.3726 (assume θ is acute).
Determine each of the following as being either true or false.In a right triangle with sides a, b, and c, and the standard angles opposite these sides, if A = 45°, then a = b.
Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points, give answers in exact form.(5, 12)
In 2000, about 70 metric tons of soil were removed from under the Leaning Tower of Pisa, and the angle the tower made with the ground was increased by about 0.5°. Before that, a point near the top
Find the values of the trigonometric functions. Round off results according to Table 4.1.sin 34.9°Data from Table 4.1 Angles and Accuracy of Trigonometric Functions Measurements of Angle to
Draw appropriate figures and verify through observation that only one triangle may contain the given parts (that is, any others which may be drawn will be congruent).A side of 4 in. included between
Draw the given angles in standard position.60°,120°,−90°
A ship’s captain, desiring to travel due south, discovers due to an improperly functioning instrument, the ship has gone 22.62 km in a direction 4.05° east of south. How far from its course (to
The straight arm of a robot is 1.25 m long and makes an angle of 13.0° above a horizontal conveyor belt. How high above the belt is the end of the arm? See Fig. 4.46. 1.25 m 13.0⁰ Fig. 4.46 Belt
Determine each of the following as being either true or false.In Example 2 of Section 4.5, if the angle of elevation from the north goal line to the blimp is 58.5°, the solution is the same.
Find the values of the trigonometric functions. Round off results according to Table 4.1.cos 72.5°Data from Table 4.1 Angles and Accuracy of Trigonometric Functions Measurements of Angle to
Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points, give answers in exact form.(15, 8)
On level ground, a tree 12.0 m high has a shadow 85.0 m long. What is the angle of elevation of the sun?
Draw appropriate figures and verify through observation that only one triangle may contain the given parts (that is, any others which may be drawn will be congruent).A right triangle with a
Draw the given angles in standard position.330°,−150°, 450°
Find tanθ in fractional form if sinθ = 2/3 (assume θ is acute).
Determine each of the following as being either true or false.If an angle has a cosine of 0.2, then the secant of the angle is 5.
Find the values of the trigonometric functions. Round off results according to Table 4.1.tan 57.6°Data from Table 4.1 Angles and Accuracy of Trigonometric Functions Measurements of Angle to
Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points, give answers in exact form.(240, 70)
Solve the right triangles with the given parts or state that there is not enough information to solve. Round off results according to Table 4.1. Refer to Fig. 4.37.A = 77.8°, a = 670̅0Data from
Solve the right triangle in Fig. 4.94 if A = 37.4° and b = 52.8. A b Fig. 4.94 B a C
Draw appropriate figures and verify through observation that only one triangle may contain the given parts (that is, any others which may be drawn will be congruent).A right triangle with a 70°
Find the values of the trigonometric functions. Round off results according to Table 4.1.sin 36.0°Data from Table 4.1 Angles and Accuracy of Trigonometric Functions Measurements of Angle to
Draw the given angles in standard position.50°,−120°,−30°
Find cscθ if tanθ = 1.294 (assume θ is acute).
Find the smallest positive angle and the smallest negative angle (numerically) coterminal with but not equal to the given angle.47.0°
Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points, give answers in exact form.(0.09, 0.40)
The headlights of an automobile are set such that the beam drops 2.00 in. for each 25.0 ft in front of the car. What is the angle between the beam and the road?
A bullet was fired such that it just grazed the top of a table. It entered a wall, which is 12.60 ft from the graze point in the table, at a point 4.63 ft above the tabletop. At what angle was the
Solve the right triangle in Fig. 4.94 if a = 2.49 and c = 3.88 A b Fig. 4.94 B a C
Solve the right triangles with the given parts or state that there is not enough information to solve. Round off results according to Table 4.1. Refer to Fig. 4.37.A = 18.4°, c = 0.0897Data from
Draw the given angles in standard position.45°, 245°,−250°
Find the values of the trigonometric functions. Round off results according to Table 4.1.cos 15.71°Data from Table 4.1 Angles and Accuracy of Trigonometric Functions Measurements of Angle to
Solve the right triangles with the given parts or state that there is not enough information to solve. Round off results according to Table 4.1. Refer to Fig. 4.37.a = 150, c = 345Data from Table
Find the smallest positive angle and the smallest negative angle (numerically) coterminal with but not equal to the given angle.338.8°
Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points, give answers in exact form.(1.1, 6.0)
In a series RL circuit, the impedance Z can be represented as the hypotenuse of a right triangle that has legs R (resistance) and XL (inductive reactance). The angle ∅ between R and Z is called the
Determine one positive and one negative coterminal angle for each angle given.125°
Find the values of the trigonometric functions. Round off results according to Table 4.1.tan 8.653°Data from Table 4.1 Angles and Accuracy of Trigonometric Functions Measurements of Angle to
Find the smallest positive angle and the smallest negative angle (numerically) coterminal with but not equal to the given angle.−217.5°
Find values of the trigonometric functions of the angle (in standard position) whose terminal side passes through the given points, give answers in exact form.(1.2, 3.5)
Determine one positive and one negative coterminal angle for each angle given.173°
The equal sides of an isosceles triangle are each 12.0, and each base angle is 42.0°. What is the length of the third side?
Find the smallest positive angle and the smallest negative angle (numerically) coterminal with but not equal to the given angle.−0.72°
Use the following table, which gives the fraction (as a decimal) of the total heating load of a certain system that will be supplied by a solar collector of area A (in m2). Find the indicated values
For the health insurance of each employee, an insurance company charges a business with fewer than 2500 employees at an annual rate (in dollars) of where x is the number of employees. Find C for
A fountain is at the center of a circular pool of radius r ft, and the area is enclosed within a circular railing that is 45.0 ft from the edge of the pool.If the total area within the railing is
Use a graphing calculator to find the range of the given functions. Use the maximum or minimum feature when needed. y = 2 x² x+1
A computer, using data from a refrigeration plant, estimates that in the event of a power failure, the temperature (in °C) in the freezers would be given bywhere t is the number of hours after the
Two electrical resistors in parallel (see Fig. 3.46) have a combined resistance RT given by If R2 = R1 + 2.0, express RT as a function of R1 and find R1 if RT = 6.0 .Fig. 3.46
Use a graphing calculator to find the range of the given functions. Use the maximum or minimum feature when needed. y = x + 1 x²

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