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mathematics
basic technical mathematics

Questions and Answers of Basic Technical Mathematics

A lawn sprinkler can water up to a distance of 65.0 ft. It turns through an angle of 115.0°. What area can it water?
Find the trigonometric functions of θ if the terminal side of θ passes through the given point. All coordinates are exact.(20,−8)
The given angles are approximate find the values of the given trigonometric functions directly from a calculator.sin(−215.5°)
The given numbers represent angle measure. Express the measure of each angle in degrees.−1.354
Express the given angles in radian measure. Round off results to the number of significant digits in the given angle.268.7°
A spotlight beam sweeps through a horizontal angle of 75.0°. If the range of the spotlight is 250 ft, what area can it cover?
Find the trigonometric functions of θ if the terminal side of θ passes through the given point. All coordinates are exact.(0.9, 4)
The given angles are approximate find θ for 0° ≤ θ < 360°.sinθ = −0.8480
Express the given angles in radian measure. Round off results to the number of significant digits in the given angle.478.5°
If a car makes a U-turn in 6.0 s, what is its average angular velocity in the turn, expressed in rad/s?
The given numbers represent angle measure. Express the measure of each angle in degrees.−36.07
For the given values, determine the quadrant(s) in which the terminal side of the angle lies.sinθ = 0.5000
The given angles are approximate find θ for 0° ≤ θ < 360°.tanθ = −1.830
What is the floor area of the hallway shown in Fig. 8.43? The outside and inside of the hallway are circular arcs. Fig. 8.43 3.755 m 7.535 m 1 8.250 m
The given numbers represent angle measure. Express the measure of each angle in degrees.14.5
Express the given angles in radian measure. Round off results to the number of significant digits in the given angle.−86.1°
A ceiling fan has blades 61.0 cm long. What is the linear velocity of the tip of a blade when the fan is rotating at 8.50 r/s?
For the given values, determine the quadrant(s) in which the terminal side of the angle lies.cosθ = 0.8666
The given angles are approximate find θ for 0° ≤ θ < 360°.cosθ = 0.4003
Express the given angles in radians (not in terms of π).102°
The given numbers express the angle measure. Express the measure of each angle in terms of degrees, with the same accuracy as the given value.0.750
For the given values, determine the quadrant(s) in which the terminal side of the angle lies.tanθ = −2.500
The given angles are approximate find θ for 0° ≤ θ < 360°.secθ = −1.637
Express the given angles in radians (not in terms of π).305°
The given numbers express the angle measure. Express the measure of each angle in terms of degrees, with the same accuracy as the given value.0.240
The arm of a car windshield wiper is 12.75 in. long and is attached at the middle of a 15.00-in. blade. (Assume that the arm and blade are in line.) What area of the windshield is cleaned by the
A wrecking ball is dropped as shown in Fig. 8.44. Its velocity at the bottom of its swing is v = √2gh, where g is the acceleration due to gravity. What is its angular velocity at the bottom if g =
For the given values, determine the quadrant(s) in which the terminal side of the angle lies.sinθ = −0.8666
The given angles are approximate find θ for 0° ≤ θ < 360°.cotθ = −0.012
Express the given angles in radians (not in terms of π).20.25°
The given numbers express the angle measure. Express the measure of each angle in terms of degrees, with the same accuracy as the given value.3.407
Part of a railroad track follows a circular arc with a central angle of 28.0°. If the radius of the arc of the inner rail is 93.67 ft and the rails are 4.71 ft apart, how much longer is the outer
For the given values, determine the quadrant(s) in which the terminal side of the angle lies.cosθ = −0.5000
The given angles are approximate find θ for 0° ≤ θ < 360°.cscθ = −8.09
Express the given angles in radians (not in terms of π).148.38°
Part of a security fence is built 2.50 m from a cylindrical storage tank 11.2 m in diameter. What is the area between the tank and this part of the fence if the central angle of the fence is 75.5°?
The given numbers express the angle measure. Express the measure of each angle in terms of degrees, with the same accuracy as the given value.1.703
For the given values, determine the quadrant(s) in which the terminal side of the angle lies.tanθ = 0.4270
The given angles are approximate find θ for 0° ≤ θ < 360°.sinθ = 0.870, cos θ < 0
Express the given angles in radians (not in terms of π).−636.2°
The given numbers express the angle measure. Express the measure of each angle in terms of degrees, with the same accuracy as the given value.12.4
Through what angle does the drum in Fig. 8.46 turn in order to lower the crate 18.5 ft? Fig. 8.46 2.38 ft Crate
Determine the quadrant in which the terminal side of θ lies, subject to both given conditions.sin θ > 0, cos θ < 0
The given angles are approximate find θ for 0° ≤ θ < 360°.tan θ = 0.932, sin θ < 0
Express the given angles in radians (not in terms of π).385.4°
The given numbers express the angle measure. Express the measure of each angle in terms of degrees, with the same accuracy as the given value.−34.4
Determine the quadrant in which the terminal side of θ lies, subject to both given conditions.tan θ > 0, cos θ < 0
The given angles are approximate find θ for 0° ≤ θ < 360°.cosθ = −0.12, tanθ > 0
Express the given angles in radian measure in terms of π.270°
The given numbers express the angle measure. Express the measure of each angle in terms of degrees, with the same accuracy as the given value.−16.42
Evaluate the given trigonometric functions by first changing the radian measure to degree measure. Round off results to four significant digits. π sin- 4
A section of road follows a circular arc with a central angle of 15.6° . The radius of the inside of the curve is 285.0 m, and the road is 15.2 m wide. What is the volume of the concrete in the road
Determine the quadrant in which the terminal side of θ lies, subject to both given conditions.secθ < 0, cot θ < 0
The given angles are approximate find θ for 0° ≤ θ < 360°.sinθ = −0.192, tanθ < 0
Express the given angles in radian measure in terms of π.210°
The given numbers express the angle measure. Express the measure of each angle in terms of degrees, with the same accuracy as the given value.100.0
The propeller of the motor on a motorboat is rotating at 130 rad/s. What is the linear velocity of a point on the tip of a blade if it is 22.5 cm long?
Determine the quadrant in which the terminal side of θ lies, subject to both given conditions.cosθ > 0, csc θ < 0
The given angles are approximate find θ for 0° ≤ θ < 360°.cscθ = −1.366, cosθ > 0
Express the given angles in radian measure in terms of π.−300°
A storm causes a pilot to follow a circular-arc route, with a central angle of 12.8° , from city A to city B rather than the straight-line route of 185.0 km. How much farther does the plane fly due
Determine the quadrant in which the terminal side of θ lies, subject to both given conditions.cscθ < 0, tanθ < 0
The given angles are approximate find θ for 0° ≤ θ < 360°.cosθ = 0.0726, sinθ < 0
Express the given angles in radian measure in terms of π.75°
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate. Express answers to four significant digits. 5π 8 sec.
Evaluate the given trigonometric functions directly, without first changing to degree measure. Round answers to three significant digits.csc 6.19
A jet is traveling westward with the sun directly overhead (the jet is on a line between the sun and the center of the Earth). How fast must the jet fly in order to keep the sun directly overhead?
In Exercises assume 0° < θ < 90°.Using the fact that sin 75° = 0.9659, evaluate cos 195°.
Find θ to four significant digits for 0 ≤ θ < 2π.sinθ = 0.3090
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate. Express answers to four significant digits. cosl-종) COS 6
A wind turbine (windmill) rotates at 40.0 r/min. What is the linear velocity of a point on the end of a blade, if the blade is 35 ft long (from the center of rotation)?
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate. Express answers to four significant digits. 23п tan- 12
Using the fact that cot 20° = 2.747, evaluate tan 290°.
Find θ to four significant digits for 0 ≤ θ < 2π.cosθ = −0.9135
A baseball field is designed such that the outfield fence is along the arc of a circle with its center at second base. If the radius of the circle is 280 ft, what is the playing area of the field?
What is the linear velocity of a point in Charleston, South Carolina, which is at a latitude of 32°46 N? The radius of the Earth is 3960 mi.
Solve the given problems assume 0° < θ < 90°.Express tan(270° − θ) in terms of the cot θ.
Find θ to four significant digits for 0 ≤ θ < 2π.tanθ = −0.2126
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate.sin 0.5906
Through what total angle does the drive shaft of a car rotate in 1s when the tachometer reads 2400 r/min?
Solve the given problems assume 0° < θ < 90°.Express cos(90° + θ) in terms of sinθ.
Find θ to four significant digits for 0 ≤ θ < 2π.sinθ = −0.0436
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate.tan 0.8035
For a triangle with angles A, B, and C, evaluate tan A + tan(B + C).
Find θ to four significant digits for 0 ≤ θ < 2π.cosθ = 0.6742
An oil storage tank 4.25 m long has a flat bottom as shown in Fig. 8.50. The radius of the circular part is 1.10 m. What volume of oil does the tank hold? Fig. 8.50 1.10 m 1.48 m 4.25 m
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate.csc 2.153
The turbine fan blade of a turbojet engine is 1.2 m in diameter and rotates at 250r/s. How fast is the tip of a blade moving?
(a) Is sin180° = 2 sin 90°? (b) Is sin360° = 2 sin180°?
Find θ to four significant digits for 0 ≤ θ < 2π.cotθ = 1.860
Determine the values of the given trigonometric functions directly on a calculator. The angles are approximate.cos (−7.190)
The force F that a rope exerts on a crate is related to force Fx directed along the x-axis by F = Fx secθ, where θ is the standard-position angle for F. See Fig. 8.18. Find F if Fx = −365 N
For the slider mechanism shown in Fig. 8.19, y sinα = x sinβ. Find y if x = 6.78 in., α = 31.3°, and β = 104.7°. α В B y Fig. 8.19 X
A patio is in the shape of a circular sector with a central angle of 160.0°. It is enclosed by a railing of which the circular part is 11.6 m long. What is the area of the patio?
The current i in an alternating-current circuit is given by i = im sinθ, where im is the maximum current in the circuit. Find i if im = 0.0259A and θ = 495.2°.
Two equal beams of light illuminate the area shown in Fig. 8.51. What area is lit by both beams?Fig. 8.51 2.70 ft 4.26 ft 2.70 ft
Find θ to four significant digits for 0 ≤ θ < 2π.secθ = −1.307
Find θ in degrees for 0° ≤ θ < 360°.tanθ = 0.1817
A laser follows the path shown in Fig. 8.20. The angle θ is related to the distances a, b, and c by 2ab cosθ = a2 + b2 − c2 . Find θ if a = 12.9 cm, b = 15.3 cm, and c = 24.5 cm. a 0 b Fig. 8.20
Find θ to four significant digits for 0 ≤ θ < 2π.cscθ = 3.940

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