 3.5.3.1.367: In this Set, round answers as necessary to three significant digits...
 3.5.3.1.368: In this Set, round answers as necessary to three significant digits...
 3.5.3.1.369: In this Set, round answers as necessary to three significant digits...
 3.5.3.1.370: In this Set, round answers as necessary to three significant digits...
 3.5.3.1.371: In this Set, round answers as necessary to three significant digits...
 3.5.3.1.372: In this Set, round answers as necessary to three significant digits...
 3.5.3.1.373: Find the distance s covered by a point moving with linear velocity ...
 3.5.3.1.374: Find the distance s covered by a point moving with linear velocity ...
 3.5.3.1.375: Find the distance s covered by a point moving with linear velocity ...
 3.5.3.1.376: Find the distance s covered by a point moving with linear velocity ...
 3.5.3.1.377: Find the distance s covered by a point moving with linear velocity ...
 3.5.3.1.378: Find the distance s covered by a point moving with linear velocity ...
 3.5.3.1.379: Point P sweeps out central angle eas it rotates on a circle ofradiu...
 3.5.3.1.380: Point P sweeps out central angle eas it rotates on a circle ofradiu...
 3.5.3.1.381: Point P sweeps out central angle eas it rotates on a circle ofradiu...
 3.5.3.1.382: Point P sweeps out central angle eas it rotates on a circle ofradiu...
 3.5.3.1.383: Point P sweeps out central angle eas it rotates on a circle ofradiu...
 3.5.3.1.384: Point P sweeps out central angle eas it rotates on a circle ofradiu...
 3.5.3.1.385: Point P sweeps out central angle eas it rotates on a circle ofradiu...
 3.5.3.1.386: Point P sweeps out central angle eas it rotates on a circle ofradiu...
 3.5.3.1.387: Rotating Light Figure 3 shows a lighthouse that is ] 00 feet from a...
 3.5.3.1.388: Rotating Light Using the diagram in Figure 3, find an equation that...
 3.5.3.1.389: In the problems that follow, point P moves with angular velocity w ...
 3.5.3.1.390: In the problems that follow, point P moves with angular velocity w ...
 3.5.3.1.391: In the problems that follow, point P moves with angular velocity w ...
 3.5.3.1.392: In the problems that follow, point P moves with angular velocity w ...
 3.5.3.1.393: In the problems that follow, point P moves with angular velocity w ...
 3.5.3.1.394: In the problems that follow, point P moves with angular velocity w ...
 3.5.3.1.395: For each of the following problems, find the angular velocity, in r...
 3.5.3.1.396: For each of the following problems, find the angular velocity, in r...
 3.5.3.1.397: For each of the following problems, find the angular velocity, in r...
 3.5.3.1.398: For each of the following problems, find the angular velocity, in r...
 3.5.3.1.399: For each of the following problems, find the angular velocity, in r...
 3.5.3.1.400: For each of the following problems, find the angular velocity, in r...
 3.5.3.1.401: For each problem below, a point is rotating with uniform circular m...
 3.5.3.1.402: For each problem below, a point is rotating with uniform circular m...
 3.5.3.1.403: For each problem below, a point is rotating with uniform circular m...
 3.5.3.1.404: For each problem below, a point is rotating with uniform circular m...
 3.5.3.1.405: For each problem below, a point is rotating with uniform circular m...
 3.5.3.1.406: For each problem below, a point is rotating with uniform circular m...
 3.5.3.1.407: Velocity at the Equator The earth rotates through one complete revo...
 3.5.3.1.408: Velocity at the Equator Assuming the radius of the earth is 4,000 m...
 3.5.3.1.409: Velocity of a Mixer Blade A mixing blade on a food processor extend...
 3.5.3.1.410: Velocity of a Lawnmower Blade A gasolinedriven lawnmower has a bla...
 3.5.3.1.411: Cable Cars The San Francisco cable cars travel by clamping onto a s...
 3.5.3.1.412: Cable Cars The Los Angeles Cable Railway was driven by a 13footdi...
 3.5.3.1.413: Cable Cars The old Sutter Street cable car line in San Francisco (F...
 3.5.3.1.414: Cable Cars The Cleveland City Cable Railway had a IAfootdiameter ...
 3.5.3.1.415: Ski Lift A ski lift operates by driving a wire rope, from which cha...
 3.5.3.1.416: Ski Uft An engineering firm is designing a ski lift. The wire rope ...
 3.5.3.1.417: Velocity ofa Ferris Wheel Figure 7 is a model of the Ferris wheel k...
 3.5.3.1.418: Velocity of a Ferris Wheel Use Figure 7 as a model of the Ferris wh...
 3.5.3.1.419: For the Ferris wheel described in 51, find the height of the rider,...
 3.5.3.1.420: For the Ferris wheel described in 52, find the height ofthe rider, ...
 3.5.3.1.421: Velocity of a Bike Wheel A woman rides a bicycle for 1 hour and tra...
 3.5.3.1.422: Velocity of a Bike Wheel Find the number of revolutions per minute ...
 3.5.3.1.423: The first gear in a singlestage gear train has 42 teeth and an ang...
 3.5.3.1.424: The second gear in a singlestage gear train has 6 teeth and an ang...
 3.5.3.1.425: A gear train consists of three gears meshed together (Figure 9). Th...
 3.5.3.1.426: A twostage gear train consists of four gears meshed together (Figu...
 3.5.3.1.427: When Lance Armstrong blazed up Mount Ventoux in the 2002 Tour, he w...
 3.5.3.1.428: On level ground, Lance would use a larger chainring and a smaller s...
 3.5.3.1.429: IfLance was using his 2IOmillimeterdiameter chainring and pedalin...
 3.5.3.1.430: If Lance was using his l50millimeterdiameter chainring and pedali...
 3.5.3.1.431: Suppose Lance was using a l50millimeterdiameter chainring and an ...
 3.5.3.1.432: Suppose Lance was using a 21Omilllmeterdiameter chainring and a 4...
 3.5.3.1.433: Magnitude ofa Vector Find the magnitudes of the horizontal and vert...
 3.5.3.1.434: Magnitude ofa Vector The magnitude of the horizontal component of a...
 3.5.3.1.435: Distance and Bearing A ship sails for 85.5 miles on a bearing of S ...
 3.5.3.1.436: Distance and Bearing A plane flying with a constant speed of 285.5 ...
 3.5.3.1.437: Winternationals Jim Rizzoli owns, maintains, and races an alcohol d...
Solutions for Chapter 3.5: Radian Measure
Full solutions for Trigonometry
ISBN: 9780495108351
Solutions for Chapter 3.5: Radian Measure
Get Full SolutionsSince 71 problems in chapter 3.5: Radian Measure have been answered, more than 32203 students have viewed full stepbystep solutions from this chapter. Trigonometry was written by and is associated to the ISBN: 9780495108351. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: . Chapter 3.5: Radian Measure includes 71 full stepbystep solutions.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Rank r (A)
= number of pivots = dimension of column space = dimension of row space.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.