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Trigonometry (MindTap Course List)

8th Edition
Charles P. McKeague + 1 other
Publisher: Cengage Learning
ISBN: 9781305652224
Chapter 3.4, Problem 73PS
Textbook Problem
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If θ = 40 ° is a central angle in a circle of radius 9 feet, find the arc length cut off by θ .

  1. 1620 ft
  2. 9 π ft
  3. 2 π ft
  4. 360 ft

To determine

To calculate:

The arc length cut off by θ in a circle where θ is 40° and radius is 9 feet.

Explanation of Solution

Given information:

The central angle of the circle, θ=40°

The radius of the circle, r=9 feet

Formula used:

For any circle with radius r and central angle θ, the length of the arc cut off by θ is s=rθ, where s is the arc length and θ is measured in radians.

For an angle 180°, the radian measure of 180° is π radians.

For an angle 1°, the radian measure of 1° is π180 radians.

For an angle θ in degrees, the radian measure of θ is θ×π180 radians.

Calculation:

Known that for an angle θ in degrees, the radian measure of θ is θ×π180 radians.

To find the radian measure of the central angle θ=40°, substitute 40° for θ in θ×π180 and simplify

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Chapter 3 Solutions

Trigonometry (MindTap Course List)
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Ch. 3.1 - Draw each of the following angles in standard...Ch. 3.1 - Draw each of the following angles in standard...Ch. 3.1 - Draw each of the following angles in standard...Ch. 3.1 - Draw each of the following angles in standard...Ch. 3.1 - Draw each of the following angles in standard...Ch. 3.1 - 120 Draw each of the following angles in standard...Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Find the exact value of each of the following....Ch. 3.1 - Use a calculator to find the following. 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Identify the function, the...Ch. 3.3 - Evaluate sin116. Identify the function, the...Ch. 3.3 - Use a calculator to approximate each value to four...Ch. 3.3 - Use a calculator to approximate each value to four...Ch. 3.3 - Use a calculator to approximate each value to four...Ch. 3.3 - Use a calculator to approximate each value to four...Ch. 3.3 - Use a calculator to approximate each value to four...Ch. 3.3 - Use a calculator to approximate each value to four...Ch. 3.3 - If we start at the point (1,0) and travel once...Ch. 3.3 - If we start at the point (1,0) and travel once...Ch. 3.3 - If we start at the point (1,0) and travel once...Ch. 3.3 - If we start at the point (1,0) and travel once...Ch. 3.3 - Which of the six trigonometric functions are not...Ch. 3.3 - Which of the six trigonometric functions are not...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - For Problems 83 through 94, determine lithe...Ch. 3.3 - 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The diagram of the unit circle shown in Figure 15...Ch. 3.3 - Problems 107 through 112 refer to right triangle...Ch. 3.3 - Problems 107 through 112 refer to right triangle...Ch. 3.3 - Problems 107 through 112 refer to right triangle...Ch. 3.3 - Problems 107 through 112 refer to right triangle...Ch. 3.3 - Problems 107 through 112 refer to right triangle...Ch. 3.3 - Problems 107 through 112 refer to right triangle...Ch. 3.3 - Use the unit circle in Figure 14 to approximate...Ch. 3.3 - If angle is in standard position and the terminal...Ch. 3.3 - Use a calculator to approximate sec4. -1.3213...Ch. 3.3 - Which statement is possible for some real number...Ch. 3.4 - For Questions 1 through 4, fill in each blank with...Ch. 3.4 - For Questions 1 through 4, fill in each blank with...Ch. 3.4 - For Questions 1 through 4, fill in each blank with...Ch. 3.4 - For Questions 1 through 4, fill in each blank with...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - For each of the following problems, is a central...Ch. 3.4 - Arc Length The minute hand of a clock is 1.2...Ch. 3.4 - Arc length The minute hand of a clock is 4.5...Ch. 3.4 - Arc Length A satellite 200 miles above the earth...Ch. 3.4 - Arc Length How long, in hours, does it take the...Ch. 3.4 - Arc Length The pendulum on a grandfather clock...Ch. 3.4 - Arc Length Find the total distance traveled in 1...Ch. 3.4 - Cable Car Drive System The current San Francisco...Ch. 3.4 - Cable Car Drive System The first cable railway to...Ch. 3.4 - Drum Brakes The Isuzu NPR 250 light truck with...Ch. 3.4 - Drum Brakes The Isuzu NPR 250 truck with automatic...Ch. 3.4 - Diameter of the Moon From the earth, the moon...Ch. 3.4 - Diameter of the Sun If the distance to the sun is...Ch. 3.4 - Repeat Example 2 from this section for the...Ch. 3.4 - Repeat Example 2 from this section for the...Ch. 3.4 - Repeat Example 2 from this section for the...Ch. 3.4 - Repeat Example 2 from this section for the...Ch. 3.4 - Ferris Wheel In Problem Set 2.3, we mentioned a...Ch. 3.4 - Ferris Wheel A Ferris Wheel called Colossus that...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - In each of the following problems, is a central...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Find the area of the sector formed by the given...Ch. 3.4 - Area of a Sector An arc of length 3 feet is cut...Ch. 3.4 - Area of a Sector A central angle of 2 radians cuts...Ch. 3.4 - Radius of a Circle If the sector formed by a...Ch. 3.4 - Arc Length What is the length of the arc cut off...Ch. 3.4 - Radius of a Circle A sector of area 2/3 square...Ch. 3.4 - Radius of a Circle A sector of area 25 square...Ch. 3.4 - Lawn Sprinkler A lawn sprinkler is located at the...Ch. 3.4 - Windshield Wiper An automobile windshield wiper 10...Ch. 3.4 - Cycling The Campagnolo Hyperon Ultra Two carbon...Ch. 3.4 - Cycling The Reynolds RZR 46 carbon wheel, which...Ch. 3.4 - Pac-Man Figure 17 shows an image of Pac-Man from...Ch. 3.4 - Coffee Filter A conical coffee filter is made from...Ch. 3.4 - Apparent Diameter As we mentioned in this section,...Ch. 3.4 - Apparent Diameter As we mentioned in this section,...Ch. 3.4 - Apparent Diameter As we mentioned in this section,...Ch. 3.4 - Apparent Diameter As we mentioned in this section,...Ch. 3.4 - Angle of Elevation If a 75-foot flagpole casts a...Ch. 3.4 - Height of a Hill A road up a hill makes an angle...Ch. 3.4 - Angle of Depression A person standing 5.2 feet...Ch. 3.4 - Distance and Bearing A boat travels on a course of...Ch. 3.4 - Geometry The height of a right circular cone is...Ch. 3.4 - Height of a Tree Two people decide to find the...Ch. 3.4 - If =40 is a central angle in a circle of radius 9...Ch. 3.4 - If =40 is a central angle in a circle of radius 9...Ch. 3.4 - A curve along a highway is an arc of a circle with...Ch. 3.4 - A lawn sprinkler has been set to rotate through an...Ch. 3.5 - For Questions 1 through 4, fill in each blank with...Ch. 3.5 - For Questions 1 through 4, fill in each blank with...Ch. 3.5 - For Questions 1 through 4, fill in each blank with...Ch. 3.5 - For Questions 1 through 4, fill in each blank with...Ch. 3.5 - Find the linear velocity of a point moving with...Ch. 3.5 - Find the linear velocity of a point moving with...Ch. 3.5 - Find the linear velocity of a point moving with...Ch. 3.5 - Find the linear velocity of a point moving with...Ch. 3.5 - Find the linear velocity of a point moving with...Ch. 3.5 - Find the linear velocity of a point moving with...Ch. 3.5 - Find the distance s covered by a point moving with...Ch. 3.5 - Find the distance s covered by a point moving with...Ch. 3.5 - Find the distance s covered by a point moving with...Ch. 3.5 - Find the distance s covered by a point moving with...Ch. 3.5 - Find the distance s covered by a point moving with...Ch. 3.5 - Find the distance s covered by a point moving with...Ch. 3.5 - Point P sweeps out central angle as it rotates on...Ch. 3.5 - Point P sweeps out central angle as it rotates on...Ch. 3.5 - Point P sweeps out central angle as it rotates on...Ch. 3.5 - Point P sweeps out central angle as it rotates on...Ch. 3.5 - Point P sweeps out central angle as it rotates on...Ch. 3.5 - Point P sweeps out central angle as it rotates on...Ch. 3.5 - Rotating Light Figure 3 shows a lighthouse that is...Ch. 3.5 - Rotating Light Using the diagram in Figure 3, find...Ch. 3.5 - In the problems that follow, point P moves with...Ch. 3.5 - In the problems that follow, point P moves with...Ch. 3.5 - In the problems that follow, point P moves with...Ch. 3.5 - In the problems that follow, point P moves with...Ch. 3.5 - In the problems that follow, point P moves with...Ch. 3.5 - In the problems that follow, point P moves with...Ch. 3.5 - For each of the following problems, find the...Ch. 3.5 - For each of the following problems, find the...Ch. 3.5 - For each of the following problems, find the...Ch. 3.5 - For each of the following problems, find the...Ch. 3.5 - For each of the following problems, find the...Ch. 3.5 - For each of the following problems, find the...Ch. 3.5 - For each of the following problems, a point is...Ch. 3.5 - For each of the following problems, a point is...Ch. 3.5 - For each of the following problems, a point is...Ch. 3.5 - For each of the following problems, a point is...Ch. 3.5 - For each of the following problems, a point is...Ch. 3.5 - For each of the following problems, a point is...Ch. 3.5 - Velocity at the Equator The earth rotates through...Ch. 3.5 - Velocity at the Equator Assuming the radius of the...Ch. 3.5 - Velocity of a Miser Blade A mixing blade on a food...Ch. 3.5 - Velocity of a Lawnmower Blade A gasoline-driven...Ch. 3.5 - Cable Cars The San Francisco cable cars travel by...Ch. 3.5 - Cable Cars The Los Angeles Cable Railway was...Ch. 3.5 - Cable Cars The Cleveland City Cable Railway had a...Ch. 3.5 - Cable Cars The old Sutter Street cable car line in...Ch. 3.5 - Ski Lift A ski lift operates by driving a wire...Ch. 3.5 - Ski Lift An engineering firm is designing a ski...Ch. 3.5 - Velocity of a Ferris Wheel Figure 7 is a model of...Ch. 3.5 - Velocity of a Ferris Wheel Use Figure 7 as a model...Ch. 3.5 - Ferris Wheel For the Ferns wheel described in...Ch. 3.5 - Ferris Wheel For the Ferris wheeI described in...Ch. 3.5 - Velocity of a Bike Wheel A woman rides a bicycle...Ch. 3.5 - Velocity of a Bike Wheel Find the number of...Ch. 3.5 - Gear Trains Figure 8 shows a single-stage gear...Ch. 3.5 - Gear Trains Figure 8 shows a single-stage gear...Ch. 3.5 - A gear train consists of three gears meshed...Ch. 3.5 - A two-stage gear train consists of four gears...Ch. 3.5 - Cycling When a cyclist pedals. he turns a gear,...Ch. 3.5 - Cycling When a cyclist pedals. he turns a gear,...Ch. 3.5 - Cycling When a cyclist pedals. he turns a gear,...Ch. 3.5 - Cycling When a cyclist pedals. he turns a gear,...Ch. 3.5 - Cycling When a cyclist pedals. he turns a gear,...Ch. 3.5 - Alcohol Dragster On board most alcohol dragsters...Ch. 3.5 - Magnitude of a Vector Find the magnitudes of the...Ch. 3.5 - Magnitude of a Vector The magnitude of the...Ch. 3.5 - Distance and Bearing A ship sails for 85.5 miles...Ch. 3.5 - Distance and Bearing A plane flying with a...Ch. 3.5 - +Find the linear velocity of a point moving with...Ch. 3.5 - Find the angular velocity of a point moving with...Ch. 3.5 - Find the linear velocity of a point rotating at 30...Ch. 3.5 - A pulley is driven by a belt moving at a speed of...Ch. 3 - Draw each of the following angles in standard...Ch. 3 - Draw each of the following angles in standard...Ch. 3 - Use a calculator to find each of the following...Ch. 3 - Use a calculator to find each of the following...Ch. 3 - Use a calculator to find each of the following...Ch. 3 - Use a calculator to find , to the nearest tenth of...Ch. 3 - Use a calculator to find , to the nearest tenth of...Ch. 3 - Give the exact value of each of the following:...Ch. 3 - Give the exact value of each of the following:...Ch. 3 - Give the exact value of each of the following:...Ch. 3 - Give the exact value of each of the following:...Ch. 3 - Give the exact value of each of the following:...Ch. 3 - Give the exact value of each of the following:...Ch. 3 - Give the exact value of each of the following: If...Ch. 3 - Give the exact value of each of the following:...Ch. 3 - Give the exact value of each of the following: Use...Ch. 3 - Determine if the statement sinz=2 is possible for...Ch. 3 - Evaluate 2cos(3x2) when x is 4.Ch. 3 - If =60o is a central angle in a circle of radius 6...Ch. 3 - If =5 is a central angle that cuts off an arc...Ch. 3 - Find the area of the sector formed by central...Ch. 3 - Distance A boy is twirling a model airplane on a...Ch. 3 - Area of a Sector A central angle of 4 radians cuts...Ch. 3 - Point P moves with angular velocity =4 radians per...Ch. 3 - For each of the following problems, a points is...Ch. 3 - For each of the following problems, a point is...Ch. 3 - Angular Velocity A belt connects a pulley of...Ch. 3 - Linear Velocity A propeller with radius 3.50 feet...Ch. 3 - Cable Cars If a 14 -foot-diameter sheave is used...Ch. 3 - Cycling A pro cyclist is riding in the Vuelta a...Ch. 3 - Determine the lengths of MO, OP, and MG. Figure 2...Ch. 3 - Find angle QOP in terms of and .Ch. 3 - Use right triangle trigonometry to find lengths a...Ch. 3 - We know that the angular velocity of the arm is 3...Ch. 3 - We know that the angular velocity of the arm is 3...Ch. 3 - Graph this function with your graphing calculator....Ch. 3 - We mentioned in Chapter 2 that the Ferris wheel...Ch. 3 - Use the information given in Figure 1 to find x,...Ch. 3 - Geometry Find the measure of one of the interior...Ch. 3 - Find the distance from the origin to the point...Ch. 3 - Find all angles that are coterminal with 150.Ch. 3 - In which quadrant will lie if sin0 and cos0?Ch. 3 - Find all six trigonometric functions for if the...Ch. 3 - Find the remaining trigonometric functions of if...Ch. 3 - If sec=4, find cos.Ch. 3 - Multiply (sin+3)(sin7).Ch. 3 - Prove that sin(csc+cot)=1+cos is an identity by...Ch. 3 - Find sinA , cosA, tanA, and sinB , cosB, and tanB...Ch. 3 - Fill in the blank to make the statement true: sec...Ch. 3 - Subtract 1532 from 2515.Ch. 3 - Use a calculator to find to the nearest tenth of...Ch. 3 - Give the number of significant digits in each...Ch. 3 - If triangle ABC is a right triangle with B=48o,...Ch. 3 - Distance and Bearing A ship leaves the harbour...Ch. 3 - Angle of Depression A man standing on the roof a...Ch. 3 - Vector Magnitude If vector V has magnitude 5.0 and...Ch. 3 - Static Equilibrium David and his sister Jessica...Ch. 3 - Draw 117.8o in standard position and then name the...Ch. 3 - Use a calculator to find , to the nearest tenth of...Ch. 3 - Convert 390o to radian measure. Write your answer...Ch. 3 - Give the exact value of sin53.Ch. 3 - Use the unit circle to find all values of between...Ch. 3 - Use the unit circle to explain how the value of...Ch. 3 - If =6 is a central angle in a circle of radius 12...Ch. 3 - Find the area of the sector formed by central...Ch. 3 - Point P moves with angular velocity 34 radians per...Ch. 3 - Velocity of a DVD A DVD, when placed in a DVD...

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