 7.1.1: What is the formula for the circumference C of a circle of radius r...
 7.1.2: If a particle has a speed of r feet per second and travels a distan...
 7.1.3: An angle is in if its vertex is at the origin of a rectangular coor...
 7.1.4: A is a positive angle whose vertex is at the center of a circle.
 7.1.5: If the radius of a circle is r and the length of the arc subtended ...
 7.1.6: On a circle of radius r, a central angle of radians subtends an arc...
 7.1.7: 180 =radians
 7.1.8: An object travels around a circle of radius r with constant speed.I...
 7.1.9: True or False The angular speed of an object traveling around a cir...
 7.1.10: True or False For circular motion on a circle of radius r, linear s...
 7.1.11: In 1122, draw each angle 30
 7.1.12: In 1122, draw each angle 60
 7.1.13: In 1122, draw each angle 135
 7.1.14: In 1122, draw each angle 120
 7.1.15: In 1122, draw each angle 450
 7.1.16: In 1122, draw each angle 540
 7.1.17: In 1122, draw each angle 3p4
 7.1.18: In 1122, draw each angle 4p3
 7.1.19: In 1122, draw each angle  p6
 7.1.20: In 1122, draw each angle  2p3
 7.1.21: In 1122, draw each angle 16p3
 7.1.22: In 1122, draw each angle 21p4
 7.1.23: In 2328, convert each angle to a decimal in degrees. Round your ans...
 7.1.24: In 2328, convert each angle to a decimal in degrees. Round your ans...
 7.1.25: In 2328, convert each angle to a decimal in degrees. Round your ans...
 7.1.26: In 2328, convert each angle to a decimal in degrees. Round your ans...
 7.1.27: In 2328, convert each angle to a decimal in degrees. Round your ans...
 7.1.28: In 2328, convert each angle to a decimal in degrees. Round your ans...
 7.1.29: In 2934, convert each angle to DMS form. Round your answer to the n...
 7.1.30: In 2934, convert each angle to DMS form. Round your answer to the n...
 7.1.31: In 2934, convert each angle to DMS form. Round your answer to the n...
 7.1.32: In 2934, convert each angle to DMS form. Round your answer to the n...
 7.1.33: In 2934, convert each angle to DMS form. Round your answer to the n...
 7.1.34: In 2934, convert each angle to DMS form. Round your answer to the n...
 7.1.35: In 3546, convert each angle in degrees to radians. Express your ans...
 7.1.36: In 3546, convert each angle in degrees to radians. Express your ans...
 7.1.37: In 3546, convert each angle in degrees to radians. Express your ans...
 7.1.38: In 3546, convert each angle in degrees to radians. Express your ans...
 7.1.39: In 3546, convert each angle in degrees to radians. Express your ans...
 7.1.40: In 3546, convert each angle in degrees to radians. Express your ans...
 7.1.41: In 3546, convert each angle in degrees to radians. Express your ans...
 7.1.42: In 3546, convert each angle in degrees to radians. Express your ans...
 7.1.43: In 3546, convert each angle in degrees to radians. Express your ans...
 7.1.44: In 3546, convert each angle in degrees to radians. Express your ans...
 7.1.45: In 3546, convert each angle in degrees to radians. Express your ans...
 7.1.46: In 3546, convert each angle in degrees to radians. Express your ans...
 7.1.47: In 4758, convert each angle in radians to degrees. p3
 7.1.48: In 4758, convert each angle in radians to degrees. 5p6
 7.1.49: In 4758, convert each angle in radians to degrees.  5p4
 7.1.50: In 4758, convert each angle in radians to degrees.  2p3
 7.1.51: In 4758, convert each angle in radians to degrees. p2
 7.1.52: In 4758, convert each angle in radians to degrees. 4p
 7.1.53: In 4758, convert each angle in radians to degrees. p12
 7.1.54: In 4758, convert each angle in radians to degrees. 5p12
 7.1.55: In 4758, convert each angle in radians to degrees.  p2
 7.1.56: In 4758, convert each angle in radians to degrees. p
 7.1.57: In 4758, convert each angle in radians to degrees.  p6
 7.1.58: In 4758, convert each angle in radians to degrees.  3p4
 7.1.59: In 5964, convert each angle in degrees to radians. Express your ans...
 7.1.60: In 5964, convert each angle in degrees to radians. Express your ans...
 7.1.61: In 5964, convert each angle in degrees to radians. Express your ans...
 7.1.62: In 5964, convert each angle in degrees to radians. Express your ans...
 7.1.63: In 5964, convert each angle in degrees to radians. Express your ans...
 7.1.64: In 5964, convert each angle in degrees to radians. Express your ans...
 7.1.65: In 6570, convert each angle in radians to degrees. Express your ans...
 7.1.66: In 6570, convert each angle in radians to degrees. Express your ans...
 7.1.67: In 6570, convert each angle in radians to degrees. Express your ans...
 7.1.68: In 6570, convert each angle in radians to degrees. Express your ans...
 7.1.69: In 6570, convert each angle in radians to degrees. Express your ans...
 7.1.70: In 6570, convert each angle in radians to degrees. Express your ans...
 7.1.71: In 7178, s denotes the length of the arc of a circle of radius r su...
 7.1.72: In 7178, s denotes the length of the arc of a circle of radius r su...
 7.1.73: In 7178, s denotes the length of the arc of a circle of radius r su...
 7.1.74: In 7178, s denotes the length of the arc of a circle of radius r su...
 7.1.75: In 7178, s denotes the length of the arc of a circle of radius r su...
 7.1.76: In 7178, s denotes the length of the arc of a circle of radius r su...
 7.1.77: In 7178, s denotes the length of the arc of a circle of radius r su...
 7.1.78: In 7178, s denotes the length of the arc of a circle of radius r su...
 7.1.79: In 7986,A denotes the area of the sector of a circle of radius r fo...
 7.1.80: In 7986,A denotes the area of the sector of a circle of radius r fo...
 7.1.81: In 7986,A denotes the area of the sector of a circle of radius r fo...
 7.1.82: In 7986,A denotes the area of the sector of a circle of radius r fo...
 7.1.83: In 7986,A denotes the area of the sector of a circle of radius r fo...
 7.1.84: In 7986,A denotes the area of the sector of a circle of radius r fo...
 7.1.85: In 7986,A denotes the area of the sector of a circle of radius r fo...
 7.1.86: In 7986,A denotes the area of the sector of a circle of radius r fo...
 7.1.87: In 8790, find the length s and area A. Round answers to three decim...
 7.1.88: In 8790, find the length s and area A. Round answers to three decim...
 7.1.89: In 8790, find the length s and area A. Round answers to three decim...
 7.1.90: In 8790, find the length s and area A. Round answers to three decim...
 7.1.91: Movement of a Minute Hand The minute hand of a clock is 6 inches lo...
 7.1.92: Movement of a Pendulum A pendulum swings through an angle of 20 eac...
 7.1.93: Area of a Sector Find the area of the sector of a circle of radius ...
 7.1.94: Area of a Sector Find the area of the sector of a circle of radius ...
 7.1.95: Watering a Lawn A water sprinkler sprays water over a distance of 3...
 7.1.96: Designing a Water Sprinkler An engineer is asked to design a water ...
 7.1.97: Motion on a Circle An object is traveling around a circle with a ra...
 7.1.98: Motion on a Circle An object is traveling around a circle with a ra...
 7.1.99: Bicycle Wheels The diameter of each wheel of a bicycle is 26 inches...
 7.1.100: Car Wheels The radius of each wheel of a car is 15 inches. If the w...
 7.1.101: In 101104, the latitude of a location L is the angle formed by a ra...
 7.1.102: In 101104, the latitude of a location L is the angle formed by a ra...
 7.1.103: In 101104, the latitude of a location L is the angle formed by a ra...
 7.1.104: In 101104, the latitude of a location L is the angle formed by a ra...
 7.1.105: Speed of the Moon The mean distance of the moon from Earth is . Ass...
 7.1.106: Speed of Earth The mean distance of Earth from the Sun is . Assumin...
 7.1.107: Pulleys Two pulleys, one with radius 2 inches and the other with ra...
 7.1.108: Ferris Wheels A neighborhood carnival has a Ferris wheel whose radi...
 7.1.109: Computing the Speed of a River Current To approximate the speed of ...
 7.1.110: Spin Balancing Tires A spin balancer rotates the wheel of a car at ...
 7.1.111: The Cable Cars of San Francisco At the Cable Car Museum you can see...
 7.1.112: Difference in Time of Sunrise Naples, Florida, is approximately 90 ...
 7.1.113: Keeping Up with the Sun How fast would you have to travel on the su...
 7.1.114: Nautical Miles A nautical mile equals the length of arc subtended b...
 7.1.115: Approximating the Circumference of Earth Eratosthenes of Cyrene (27...
 7.1.116: Designing a Little League Field For a 60foot Little League Basebal...
 7.1.117: Pulleys Two pulleys, one with radius and the other with radius , ar...
 7.1.118: Do you prefer to measure angles using degrees or radians? Provide j...
 7.1.119: What is 1 radian? What is 1 degree?
 7.1.120: Which angle has the larger measure: 1 degree or 1 radian? Or are th...
 7.1.121: Explain the difference between linear speed and angular speed.
 7.1.122: For a circle of radius r, a central angle of degrees subtends an ar...
 7.1.123: Discuss why ships and airplanes use nautical miles to measure dista...
 7.1.124: Investigate the way that speed bicycles work. In particular, explai...
 7.1.125: In Example 6, we found that the distance between Albuquerque, New M...
Solutions for Chapter 7.1: Algebra and Trigonometry 9th Edition
Full solutions for Algebra and Trigonometry  9th Edition
ISBN: 9780321716569
Solutions for Chapter 7.1
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Algebra and Trigonometry was written by and is associated to the ISBN: 9780321716569. Since 125 problems in chapter 7.1 have been answered, more than 61429 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 9. Chapter 7.1 includes 125 full stepbystep solutions.

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

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

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).

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

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

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

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

Outer product uv T
= column times row = rank one matrix.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

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

Reflection matrix (Householder) Q = I 2uuT.
Unit vector u is reflected to Qu = u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q1 = Q.

Right inverse A+.
If A has full row rank m, then A+ = AT(AAT)l has AA+ = 1m.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.