 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 10629 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.

Column space C (A) =
space of all combinations of the columns of 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).

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

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

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

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).

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

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).

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

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

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.