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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

The given angles are in standard position. Designate each angle by the quadrant in which the terminal side lies, or as a quadrantal angle.180°, 92°
Use a calculator to verify the given relationships or statements. [sin2θ = (sinθ)2]sin 78.4° = 2(sin 39.2°)(cos 39.2°)
Find the values of the trigonometric functions. Round off results according to Table 4.1.csc 76.30°Data from Table 4.1 Angles and Accuracy of Trigonometric Functions Measurements of Angle to
Find θ for each of the given trigonometric functions. Assume θ is an acute angle. Round off results.cscθ = 1.92
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 = 74.18°, b = 1.849Data from
Use a calculator conversion sequence to change the given angles in radians to equal angles expressed in degrees to the nearest 0.01°.2.089 rad
A street light is designed as shown in Fig. 4.52. How high above the street is the light? 12.5 ft 20.0° 28.0 ft Fig. 4.52
Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.cosθ = 0.3261Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
Determine the trigonometric functions of the angles (in standard position) whose terminal side passes through the given points. Give answers in exact form.(5, 4)
Find the values of the indicated functions assuming θ is an acute angle. Give answers in exact form.Given sin θ = 1/2, find cosθ and cscθ.
Use a calculator conversion sequence to change the given angles in radians to equal angles expressed in degrees to the nearest 0.01°.−4.110 rad
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 = 51.36°, a = 3692Data from
Determine the trigonometric functions of the angles (in standard position) whose terminal side passes through the given points. Give answers in exact form.(48, 48)
Find the values of the indicated functions assuming θ is an acute angle. Give answers in exact form.Given tanθ = 2, find sinθ and secθ.
Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.tanθ = 2.4701Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
A straight driveway is 85.0 ft long, and the top is 12.0 ft above the bottom. What angle does it make with the horizontal?
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 = 591.87, b = 264.93Data from
Use a calculator conversion sequence to change the given angles in radians to equal angles expressed in degrees to the nearest 0.01°.6.705 rad
Part of the Tower Bridge in London is a drawbridge. This part of the bridge is 76.0 m long. When each half is raised, the distance between them is 8.0 m. What angle does each half make with the
Determine the trigonometric functions of the angles (in standard position) whose terminal side passes through the given points. Give answers in exact form.(0.36, 0.77)
Find the values of the indicated functions assuming θ is an acute angle. Give answers in exact form.Given secθ = √5/2, find tanθ and cosθ.
Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.sinθ = 0.9114Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
The angle of inclination of a road is often expressed as percent grade, which is the vertical rise divided by the horizontal run (expressed as a percent). See Fig. 4.54. A 6.0% grade corresponds to a
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 = 2.9507, c = 50.864Data from
Use a calculator conversion sequence to change the given angles to equal angles expressed in radians to three significant digits.85.0°
Find the indicated trigonometric functions. Give answers in decimal form, rounded off to three significant digits. Assume θ is an acute angle.Given sinθ = 5/13, find cosθ and cot θ.
Find the values of the indicated functions assuming θ is an acute angle, the values are approximate.Given sinθ = 0.750, find cot θ and cscθ.
Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.cosθ = 0.0427Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
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 = 2.975°, b = 14.592Data from
Use a calculator conversion sequence to change the given angles to equal angles expressed in radians to three significant digits.237.4°
Find the indicated trigonometric functions. Give answers in decimal form, rounded off to three significant digits. Assume θ is an acute angle.Given cosθ = 3/8, find sinθ and tanθ.
Find the values of the indicated functions assuming θ is an acute angle, the values are approximate.Given cosθ = 0.0326, find sinθ and tanθ.
Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.tanθ = 0.317Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
A circular patio table of diameter 1.20 m has a regular octagon design inscribed within the outer edge (all eight vertices touch the circle). What is the perimeter of the octagon?
Use a calculator conversion sequence to change the given angles to equal angles expressed in radians to three significant digits.384.8°
A square wire loop is rotating in the magnetic field between two poles of a magnet in order to induce an electric current. The axis of rotation passes through the center of the loop and is midway
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 = 84.942°, a = 7413.5Data from
Find the indicated trigonometric functions. Give answers in decimal form, rounded off to three significant digits. Assume θ is an acute angle.Given tanθ = 2, find cosθ and cscθ.
Find the values of the indicated functions assuming θ is an acute angle, the values are approximate.Given cot θ = 0.254, find cosθ and tanθ.
Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.sinθ = 1.09Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
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 = 9.56°, c = 0.0973Data from
Use a calculator conversion sequence to change the given angles to equal angles expressed in radians to three significant digits.−117.5°
Find the indicated trigonometric functions. Give answers in decimal form, rounded off to three significant digits. Assume θ is an acute angle.Given cot θ = 40, find sinθ and secθ.
Find the values of the indicated functions assuming θ is an acute angle, the values are approximate.Given cscθ = 1.20, find secθ and cosθ.
Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.cosθ = 0.65007Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
From a space probe circling Io, one of Jupiter’s moons, at an altitude of 552 km, it was observed that the angle of depression of the horizon was 39.7°. What is the radius of Io?
Change the given angles to equal angles expressed to the nearest minute.47.50°
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 = 1.28, b = 16.3Data from Table
Find the indicated trigonometric functions. Give answers in decimal form, rounded off to three significant digits. Assume θ is an acute angle.Given cosθ = 0.327, find sinθ and cscθ.
Each given point is on the terminal side of an angle. Show that each of the given functions is the same for each point.(3, 4), (6, 8), (4.5, 6), sinθ and tanθ
Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.tanθ = 5.7706Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
A manufacturing plant is designed to be in the shape of a regular pentagon with 92.5 ft on each side. A security fence surrounds the building to form a circle, and each corner of the building is 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 = 35.0, C = 90.0°Data from Table
Change the given angles to equal angles expressed to the nearest minute.715.80°
A surveyor on the New York City side of the Hudson River wishes to find the height of a cliff (the Palisades) on the New Jersey side. Figure 4.56 shows the measurements that were made. How high is
Find the indicated trigonometric functions. Give answers in decimal form, rounded off to three significant digits. Assume θ is an acute angle.Given cscθ = 3.41, find tanθ and secθ.
Each given point is on the terminal side of an angle. Show that each of the given functions is the same for each point.(5, 12), (15, 36), (7.5, 18), cosθ and cot θ
Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.cscθ = 2.574Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
Change the given angles to equal angles expressed to the nearest minute.−5.62°
Find the values of the trigonometric functions. Round off results.sin 72.1°
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 = 25.7°, B = 64.3°Data from
Each given point is on the terminal side of an angle. Show that each of the given functions is the same for each point.(0.3, 0.1), (9, 3), (33, 11), tanθ and secθ
The ratio of the width to the height of a TV screen is 16 to 9. What is the angle between the width and a diagonal of the screen.
Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.secθ = 2.045Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.cot θ = 0.0606Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
Find the part of the triangle labeled either x or A in the indicated figure.Fig. 4.38(a) (a) x 3.92 61.7°
Use the unit circle to complete Exercises (see Example 5).Find cos 0°.Data from Example 5(a) Use the unit circle to find cos 90° and sin 90°. A 90° angle, when placed in standard position,
Change the given angles to equal angles expressed to the nearest minute.142.87°
Find the values of the trigonometric functions. Round off results.cos 40.3°
Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.cscθ = 1.002Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
Each given point is on the terminal side of an angle. Show that each of the given functions is the same for each point.(40, 30), (56, 42), (36, 27), cscθ and cosθ
When the distance from Earth to the sun is 94,500,000 mi, the angle that the sun subtends on Earth is 0.522°. Find the diameter of the sun.
Find the part of the triangle labeled either x or A in the indicated figure.Fig. 4.38(b) A 36.3 (b) 19.7
Change the given angles to equal angles expressed in decimal form to the nearest 0.01°.15°12´
Use the unit circle to complete Exercises (see Example 5).Find sin 0°.Data from Example 5(a) Use the unit circle to find cos 90° and sin 90°. A 90° angle, when placed in standard position,
Find the values of the trigonometric functions. Round off results.tan 85.68°
Two ladders, each 6.50 m long are leaning against opposite walls of a level alley, with their feet touching. If they make angles of 38.0° and 68.0° with respect to the alley floor, how wide is the
A TV screen is 116 cm wide and 65.3 cm high. A person is seated at an angle from the screen such that the near end of the screen is 224 cm away, and the far end is 302 cm away. If the person’s eye
Change the given angles to equal angles expressed in decimal form to the nearest 0.01°.517°39´
Find the part of the triangle labeled either x or A in the indicated figure.Fig. 4.38(c) (c) 0.6673 0.8742 A
Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.secθ = 0.305Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
Find the part of the triangle labeled either x or A in the indicated figure.Fig. 4.38(d) (d) 22.45° 7265 x
Find the values of the trigonometric functions. Round off results.sin 0.91°
If the angle θ intersects the unit circle at exactly (0.28, 0.96), find sinθ and cscθ.Data from Example 5(a) Use the unit circle to find cos 90° and sin 90°. A 90° angle, when placed in
A tract of land is in the shape of a trapezoid as shown in Fig. 4.59. Find the lengths of the nonparallel sides. 69.2⁰ 68.7 m 148 m Fig. 4.59 41.7°
Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.cot θ = 14.4Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
Change the given angles to equal angles expressed in decimal form to the nearest 0.01°.301°16´
Find the values of the trigonometric functions. Round off results.sec 36.2°
A stairway 1.0 m wide goes from the bottom of a cylindrical storage tank to the top at a point halfway around the tank. The handrail on the outside of the stairway makes an angle of 31.8° with the
Change the given angles to equal angles expressed in decimal form to the nearest 0.01°.−94°47´
For the angle in Exercise 33, find cosθ and secθ.Data from Exercises 33If the angle θ intersects the unit circle at exactly (0.28, 0.96), find sinθ and cscθ.Data from Example 5(a) Use the unit
Find the values of the trigonometric functions. Round off results.csc 82.4°
The political banner shown in Fig. 4.65 is in the shape of a parallelogram. Find its area.Fig. 4.65. 48 cm 85⁰ USE YOUR RIGHT TO VOTE 92 cm
Find the acute angle θ for each of the given trigonometric functions. Round off results according to Table 4.1.cscθ = 8.26Data from Table 4.1 Angles and Accuracy of Trigonometric Functions
Find the indicated part of the right triangle that has the given parts.One leg is 23.7, and the hypotenuse is 37.5. Find the smaller acute angle.
An antenna was on the top of the World Trade Center (before it was destroyed in 2001). From a point on the river 7800 ft from the Center, the angles of elevation of the top and bottom of the antenna
Draw angles in standard position such that the terminal side passes through the given point.(4, 2)
Find the values of the trigonometric functions. Round off results.(cot 7.06°)(sin 7.06°) − cos 7.06°
For an acute angle A, which is greater, sin A or tan A?
Find the indicated part of the right triangle that has the given parts.One leg is 8.50, and the angle opposite this leg is 52.3°. Find the other leg.

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