 2.2.1: Match each angle in Column I with its reference angle in Column II....
 2.2.2: Match each angle in Column I with its reference angle in Column II....
 2.2.3: Match each angle in Column I with its reference angle in Column II....
 2.2.4: Match each angle in Column I with its reference angle in Column II....
 2.2.5: Match each angle in Column I with its reference angle in Column II....
 2.2.6: Match each angle in Column I with its reference angle in Column II....
 2.2.7: In Example 2, why was 2 a good choice for r? Could any other positi...
 2.2.8: Explain how the reference angle is used to find values of the trigo...
 2.2.9: Explain why two coterminal angles have the same values for their tr...
 2.2.10: Explain the process for determining the sign of the sine, cosine, a...
 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 for each angle...
 2.2.20: Find exact values of the six trigonometric functions for each angle...
 2.2.21: Find exact values of the six trigonometric functions for each angle...
 2.2.22: Find exact values of the six trigonometric functions for each angle...
 2.2.23: Find exact values of the six trigonometric functions for each angle...
 2.2.24: Find exact values of the six trigonometric functions for each angle...
 2.2.25: Find exact values of the six trigonometric functions for each angle...
 2.2.26: Find exact values of the six trigonometric functions for each angle...
 2.2.27: Find exact values of the six trigonometric functions for each angle...
 2.2.28: Find exact values of the six trigonometric functions for each angle...
 2.2.29: Find exact values of the six trigonometric functions for each angle...
 2.2.30: Find exact values of the six trigonometric functions for each angle...
 2.2.31: Find exact values of the six trigonometric functions for each angle...
 2.2.32: Find exact values of the six trigonometric functions for each angle...
 2.2.33: Find exact values of the six trigonometric functions for each angle...
 2.2.34: Find exact values of the six trigonometric functions for each angle...
 2.2.35: Find exact values of the six trigonometric functions for each angle...
 2.2.36: Find exact values of the six trigonometric functions for 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 of the following. See Example 4. sin2 120 + cos2 120
 2.2.46: Evaluate each of the following. See Example 4. sin2 225 + cos2 225
 2.2.47: Evaluate each of the following. See Example 4. 2 tan2 120 + 3 sin2 ...
 2.2.48: Evaluate each of the following. See Example 4. cot2 135  sin 30 + ...
 2.2.49: Evaluate each of the following. See Example 4. sin2 225  cos2 270 ...
 2.2.50: Evaluate each of the following. See Example 4. cot2 90  sec2 180 +...
 2.2.51: Evaluate each of the following. See Example 4. cos2 60 + sec2 150 ...
 2.2.52: Evaluate each of the following. See Example 4. cot2 135 + tan4 60 ...
 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: Concept Check Find the coordinates of the point P on the circumfere...
 2.2.62: Concept Check Find the coordinates of the point P on the circumfere...
 2.2.63: Concept Check Does there exist an angle u with the function values ...
 2.2.64: Concept Check Does there exist an angle u with the function values ...
 2.2.65: Suppose u is in the interval 190, 1802 . Find the sign of each of t...
 2.2.66: Suppose u is in the interval 190, 1802 . Find the sign of each of t...
 2.2.67: Suppose u is in the interval 190, 1802 . Find the sign of each of t...
 2.2.68: Suppose u is in the interval 190, 1802 . Find the sign of each of t...
 2.2.69: Suppose u is in the interval 190, 1802 . Find the sign of each of t...
 2.2.70: Suppose u is in the interval 190, 1802 . Find the sign of each of t...
 2.2.71: Explain why sin u = sin1u + n # 3602 is true for any angle u and an...
 2.2.72: Explain why cos u = cos1u + n # 3602 is true for any angle u and an...
 2.2.73: Explain why tan u = tan(u + n # 180_) is true for any angle u and a...
 2.2.74: Without using a calculator, determine which of the following number...
 2.2.75: Without using a calculator, determine which of the following number...
 2.2.76: For what angles u between 0 and 360 is cos u =  sin u true?
 2.2.77: For what angles u between 0 and 360 is cos u = sin u true?
 2.2.78: (Modeling) Length of a Sag Curve When a highway goes downhill and t...
 2.2.79: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.80: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.81: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.82: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.83: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.84: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.85: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.86: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.87: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.88: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.89: Find all values of u, if u is in the interval 30, 3602 and has the ...
 2.2.90: Find all values of u, if u is in the interval 30, 3602 and has the ...
Solutions for Chapter 2.2: Trigonometric Functions of NonAcute Angles
Full solutions for Trigonometry  10th Edition
ISBN: 9780321671776
Solutions for Chapter 2.2: Trigonometric Functions of NonAcute Angles
Get Full SolutionsSince 90 problems in chapter 2.2: Trigonometric Functions of NonAcute Angles have been answered, more than 35410 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: 10. Chapter 2.2: Trigonometric Functions of NonAcute Angles includes 90 full stepbystep solutions. Trigonometry was written by and is associated to the ISBN: 9780321671776.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

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.

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

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).

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.

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

Hilbert matrix hilb(n).
Entries HU = 1/(i + j 1) = Jd X i 1 xj1dx. Positive definite but extremely small Amin and large condition number: H is illconditioned.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Iterative method.
A sequence of steps intended to approach the desired solution.

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

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.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

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.

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

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.

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).