 3.2.3.1.91: Find the radian measure of angle e, if eis a central angle in a cir...
 3.2.3.1.92: Find the radian measure of angle e, if eis a central angle in a cir...
 3.2.3.1.93: Find the radian measure of angle e, if eis a central angle in a cir...
 3.2.3.1.94: Find the radian measure of angle e, if eis a central angle in a cir...
 3.2.3.1.95: Find the radian measure of angle e, if eis a central angle in a cir...
 3.2.3.1.96: Find the radian measure of angle e, if eis a central angle in a cir...
 3.2.3.1.97: Angle Between Cities Los Angeles and San Francisco are approximatel...
 3.2.3.1.98: Angle Between Cities Los Angeles and New York City are approximatel...
 3.2.3.1.99: For each angle below a. Draw the angle in standard position. b. Con...
 3.2.3.1.100: For each angle below a. Draw the angle in standard position. b. Con...
 3.2.3.1.101: For each angle below a. Draw the angle in standard position. b. Con...
 3.2.3.1.102: For each angle below a. Draw the angle in standard position. b. Con...
 3.2.3.1.103: For each angle below a. Draw the angle in standard position. b. Con...
 3.2.3.1.104: For each angle below a. Draw the angle in standard position. b. Con...
 3.2.3.1.105: For each angle below a. Draw the angle in standard position. b. Con...
 3.2.3.1.106: For each angle below a. Draw the angle in standard position. b. Con...
 3.2.3.1.107: For 1720, use 3.1416 for 7T unless your calculator has a key marke...
 3.2.3.1.108: For 1720, use 3.1416 for 7T unless your calculator has a key marke...
 3.2.3.1.109: For 1720, use 3.1416 for 7T unless your calculator has a key marke...
 3.2.3.1.110: For 1720, use 3.1416 for 7T unless your calculator has a key marke...
 3.2.3.1.111: Nautical Miles If a central angle with its vertex at the center of ...
 3.2.3.1.112: Nautical Miles If a central angle with its vertex at the center of ...
 3.2.3.1.113: Nautical Miles If a central angle with its vertex at the center of ...
 3.2.3.1.114: Nautical Miles If a central angle with its vertex at the center of ...
 3.2.3.1.115: Nautical Miles If a central angle with its vertex at the center of ...
 3.2.3.1.116: Nautical Miles If a central angle with its vertex at the center of ...
 3.2.3.1.117: Simplify each expression.1T
 3.2.3.1.118: Simplify each expression.1T + 6"
 3.2.3.1.119: Simplify each expression.21T
 3.2.3.1.120: Simplify each expression. 21T
 3.2.3.1.121: Simplify each expression. + 2
 3.2.3.1.122: Simplify each expression.6"3
 3.2.3.1.123: Simplify each expression.51T
 3.2.3.1.124: Simplify each expression.31T 1T
 3.2.3.1.125: Write each angle as a sum or difference involving 1T. For example, ...
 3.2.3.1.126: Write each angle as a sum or difference involving 1T. For example, ...
 3.2.3.1.127: Write each angle as a sum or difference involving 1T. For example, ...
 3.2.3.1.128: Write each angle as a sum or difference involving 1T. For example, ...
 3.2.3.1.129: Write each angle as a difference involving 21T. For example, 51T/3 ...
 3.2.3.1.130: Write each angle as a difference involving 21T. For example, 51T/3 ...
 3.2.3.1.131: For each angle below, a. Draw the angle in standard position. b. Co...
 3.2.3.1.132: For each angle below, a. Draw the angle in standard position. b. Co...
 3.2.3.1.133: For each angle below, a. Draw the angle in standard position. b. Co...
 3.2.3.1.134: For each angle below, a. Draw the angle in standard position. b. Co...
 3.2.3.1.135: For each angle below, a. Draw the angle in standard position. b. Co...
 3.2.3.1.136: For each angle below, a. Draw the angle in standard position. b. Co...
 3.2.3.1.137: For each angle below, a. Draw the angle in standard position. b. Co...
 3.2.3.1.138: For each angle below, a. Draw the angle in standard position. b. Co...
 3.2.3.1.139: Use a calculator to convert each of the following to degree measure...
 3.2.3.1.140: Use a calculator to convert each of the following to degree measure...
 3.2.3.1.141: Use a calculator to convert each of the following to degree measure...
 3.2.3.1.142: Use a calculator to convert each of the following to degree measure...
 3.2.3.1.143: Give the exact value of each of the following: sin 3
 3.2.3.1.144: Give the exact value of each of the following: cos :3
 3.2.3.1.145: Give the exact value of each of the following: tan 6
 3.2.3.1.146: Give the exact value of each of the following: cot 3
 3.2.3.1.147: Give the exact value of each of the following: sec
 3.2.3.1.148: Give the exact value of each of the following: csc 2
 3.2.3.1.149: Give the exact value of each of the following: csc 60. sec 6 3 6
 3.2.3.1.150: Give the exact value of each of the following: sec 6
 3.2.3.1.151: Give the exact value of each of the following: sin 4
 3.2.3.1.152: Give the exact value of each of the following: cos 4
 3.2.3.1.153: Give the exact value of each of the following: 2 cos 6
 3.2.3.1.154: Give the exact value of each of the following: 2 sin 6
 3.2.3.1.155: Give the exact value of each of the following: 4 sin f
 3.2.3.1.156: Give the exact value of each of the following: 4 cos (  ;)
 3.2.3.1.157: Evaluate each of the following expressions when x is 1T/6. In each ...
 3.2.3.1.158: Evaluate each of the following expressions when x is 1T/6. In each ...
 3.2.3.1.159: Evaluate each of the following expressions when x is 1T/6. In each ...
 3.2.3.1.160: Evaluate each of the following expressions when x is 1T/6. In each ...
 3.2.3.1.161: Evaluate each of the following expressions when x is 1T/6. In each ...
 3.2.3.1.162: Evaluate each of the following expressions when x is 1T/6. In each ...
 3.2.3.1.163: Evaluate each of the following expressions when x is 1T/6. In each ...
 3.2.3.1.164: Evaluate each of the following expressions when x is 1T/6. In each ...
 3.2.3.1.165: Evaluate each of the following expressions when x is 1T/6. In each ...
 3.2.3.1.166: Evaluate each of the following expressions when x is 1T/6. In each ...
 3.2.3.1.167: Evaluate each of the following expressions when x is 1T/6. In each ...
 3.2.3.1.168: Evaluate each of the following expressions when x is 1T/6. In each ...
 3.2.3.1.169: For the following expressions, find the value of y that corresponds...
 3.2.3.1.170: For the following expressions, find the value of y that corresponds...
 3.2.3.1.171: For the following expressions, find the value of y that corresponds...
 3.2.3.1.172: For the following expressions, find the value of y that corresponds...
 3.2.3.1.173: For the following expressions, find the value of y that corresponds...
 3.2.3.1.174: For the following expressions, find the value of y that corresponds...
 3.2.3.1.175: For the following expressions, find the value of y that corresponds...
 3.2.3.1.176: For the following expressions, find the value of y that corresponds...
 3.2.3.1.177: For the following expressions, find the value of y that corresponds...
 3.2.3.1.178: For the following expressions, find the value of y that corresponds...
 3.2.3.1.179: For the following expressions, find the value of y that corresponds...
 3.2.3.1.180: For the following expressions, find the value of y that corresponds...
 3.2.3.1.181: For the following expressions, find the value of y that corresponds...
 3.2.3.1.182: For the following expressions, find the value of y that corresponds...
 3.2.3.1.183: For the following expressions, find the value of y that corresponds...
 3.2.3.1.184: For the following expressions, find the value of y that corresponds...
 3.2.3.1.185: Cycling The Campagnolo Hyperon carbon wheel has 22 spokes evenly di...
 3.2.3.1.186: Cycling The Reynolds Stratus DV carbon wheel has 16 spokes evenly d...
 3.2.3.1.187: Navigation The formula to determine the great circle distance betwe...
 3.2.3.1.188: Navigation The formula to determine the great circle distance betwe...
 3.2.3.1.189: The problems that follow review material we covered in Section 1.3....
 3.2.3.1.190: The problems that follow review material we covered in Section 1.3....
 3.2.3.1.191: Find the remaining trigonometric functions of e, if sin e ~ and ete...
 3.2.3.1.192: Find the remaining trigonometric functions of e, if cos e = l/v2 a...
 3.2.3.1.193: Find the six trigonometric functions of e, if the terminal side of ...
 3.2.3.1.194: Find the six trigonometric functions of e, if the terminal side of ...
Solutions for Chapter 3.2: Radian Measure
Full solutions for Trigonometry
ISBN: 9780495108351
Solutions for Chapter 3.2: Radian Measure
Get Full SolutionsTrigonometry was written by and is associated to the ISBN: 9780495108351. Since 104 problems in chapter 3.2: Radian Measure have been answered, more than 29940 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 3.2: Radian Measure includes 104 full stepbystep solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: .

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

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).

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

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.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

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

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

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

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Solvable system Ax = b.
The right side b is in the column space of A.