 2.2.1: The value of sin 240 is because 240 is in quadrant . (positive/nega...
 2.2.2: The value of cos 390 is because 390 is in quadrant . (positive/nega...
 2.2.3: The value of tan11502 is because 150 is in quadrant (positive/neg...
 2.2.4: The value of sec 135 is because 135 is in quadrant . (positive/nega...
 2.2.5: Concept Check Match each angle in Column I with its reference angle...
 2.2.6: Concept Check Match each angle in Column I with its reference angle...
 2.2.7: Concept Check Match each angle in Column I with its reference angle...
 2.2.8: Concept Check Match each angle in Column I with its reference angle...
 2.2.9: Concept Check Match each angle in Column I with its reference angle...
 2.2.10: Concept Check Match each angle in Column I with its reference angle...
 2.2.11: Complete the table with exact trigonometric function values. Do not...
 2.2.12: Complete the table with exact trigonometric function values. Do not...
 2.2.13: Complete the table with exact trigonometric function values. Do not...
 2.2.14: Complete the table with exact trigonometric function values. Do not...
 2.2.15: Complete the table with exact trigonometric function values. Do not...
 2.2.16: Complete the table with exact trigonometric function values. Do not...
 2.2.17: Complete the table with exact trigonometric function values. Do not...
 2.2.18: Complete the table with exact trigonometric function values. Do not...
 2.2.19: Find exact values of the six trigonometric functions of each angle....
 2.2.20: Find exact values of the six trigonometric functions of each angle....
 2.2.21: Find exact values of the six trigonometric functions of each angle....
 2.2.22: Find exact values of the six trigonometric functions of each angle....
 2.2.23: Find exact values of the six trigonometric functions of each angle....
 2.2.24: Find exact values of the six trigonometric functions of each angle....
 2.2.25: Find exact values of the six trigonometric functions of each angle....
 2.2.26: Find exact values of the six trigonometric functions of each angle....
 2.2.27: Find exact values of the six trigonometric functions of each angle....
 2.2.28: Find exact values of the six trigonometric functions of each angle....
 2.2.29: Find exact values of the six trigonometric functions of each angle....
 2.2.30: Find exact values of the six trigonometric functions of each angle....
 2.2.31: Find exact values of the six trigonometric functions of each angle....
 2.2.32: Find exact values of the six trigonometric functions of each angle....
 2.2.33: Find exact values of the six trigonometric functions of each angle....
 2.2.34: Find exact values of the six trigonometric functions of each angle....
 2.2.35: Find exact values of the six trigonometric functions of each angle....
 2.2.36: Find exact values of the six trigonometric functions of each angle....
 2.2.37: Find the exact value of each expression. See Example 3. sin 1305
 2.2.38: Find the exact value of each expression. See Example 3. sin 1500
 2.2.39: Find the exact value of each expression. See Example 3. cos15102
 2.2.40: Find the exact value of each expression. See Example 3. tan110202
 2.2.41: Find the exact value of each expression. See Example 3. csc18552
 2.2.42: Find the exact value of each expression. See Example 3. sec14952
 2.2.43: Find the exact value of each expression. See Example 3. tan 3015
 2.2.44: Find the exact value of each expression. See Example 3. cot 2280
 2.2.45: Evaluate each expression. See Example 4 sin2 120 + cos2 120
 2.2.46: Evaluate each expression. See Example 4 sin2 225 + cos2 225
 2.2.47: Evaluate each expression. See Example 4 2 tan2 120 + 3 sin2 150  c...
 2.2.48: Evaluate each expression. See Example 4 cot2 135  sin 30 + 4 tan 45
 2.2.49: Evaluate each expression. See Example 4 sin2 225  cos2 270 + tan2 60
 2.2.50: Evaluate each expression. See Example 4 cot2 90  sec2 180 + csc2 135
 2.2.51: Evaluate each expression. See Example 4 cos2 60 + sec2 150  csc2 210
 2.2.52: Evaluate each expression. See Example 4 cot2 135 + tan4 60  sin4 180
 2.2.53: Determine whether each statement is true or false. If false, tell w...
 2.2.54: Determine whether each statement is true or false. If false, tell w...
 2.2.55: Determine whether each statement is true or false. If false, tell w...
 2.2.56: Determine whether each statement is true or false. If false, tell w...
 2.2.57: Determine whether each statement is true or false. If false, tell w...
 2.2.58: Determine whether each statement is true or false. If false, tell w...
 2.2.59: Determine whether each statement is true or false. If false, tell w...
 2.2.60: Determine whether each statement is true or false. If false, tell w...
 2.2.61: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.62: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.63: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.64: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.65: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.66: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.67: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.68: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.69: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.70: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.71: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.72: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.73: Concept Check Find the coordinates of the point P on the circumfere...
 2.2.74: Concept Check Find the coordinates of the point P on the circumfere...
 2.2.75: Concept Check Does there exist an angle u with the function values ...
 2.2.76: Concept Check Does there exist an angle u with the function values ...
 2.2.77: Suppose u is in the interval 190, 1802 . Find the sign of each of t...
 2.2.78: Suppose u is in the interval 190, 1802 . Find the sign of each of t...
 2.2.79: Suppose u is in the interval 190, 1802 . Find the sign of each of t...
 2.2.80: Suppose u is in the interval 190, 1802 . Find the sign of each of t...
 2.2.81: Suppose u is in the interval 190, 1802 . Find the sign of each of t...
 2.2.82: Suppose u is in the interval 190, 1802 . Find the sign of each of t...
 2.2.83: Concept Check Work each problem Why is sin u = sin1u + n # 3602 tru...
 2.2.84: Concept Check Work each problem Why is cos u = cos1u + n # 3602 tru...
 2.2.85: Concept Check Work each problem Without using a calculator, determi...
 2.2.86: Concept Check Work each problem Without using a calculator, determi...
 2.2.87: Concept Check Work each problem For what angles u between 0 and 360...
 2.2.88: Concept Check Work each problem For what angles u between 0 and 360...
Solutions for Chapter 2.2: Trigonometric Functions of NonAcute Angles
Full solutions for Trigonometry  11th Edition
ISBN: 9780134217437
Solutions for Chapter 2.2: Trigonometric Functions of NonAcute Angles
Get Full SolutionsSince 88 problems in chapter 2.2: Trigonometric Functions of NonAcute Angles have been answered, more than 25873 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Trigonometry, edition: 11. Chapter 2.2: Trigonometric Functions of NonAcute Angles includes 88 full stepbystep solutions. Trigonometry was written by and is associated to the ISBN: 9780134217437. This expansive textbook survival guide covers the following chapters and their solutions.

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

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).

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

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

Free variable Xi.
Column i has no pivot in elimination. We can give the n  r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

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

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.

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.

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.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

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

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.