 5.4.1: Match each expression in Column I with the correct expression in Co...
 5.4.2: Match each expression in Column I with the correct expression in Co...
 5.4.3: Match each expression in Column I with the correct expression in Co...
 5.4.4: Match each expression in Column I with the correct expression in Co...
 5.4.5: Match each expression in Column I with its equivalent expression in...
 5.4.6: Match each expression in Column I with its equivalent expression in...
 5.4.7: Match each expression in Column I with its equivalent expression in...
 5.4.8: Match each expression in Column I with its equivalent expression in...
 5.4.9: Find the exact value of each expression. See Example 1. sin 165
 5.4.10: Find the exact value of each expression. See Example 1. sin 255
 5.4.11: Find the exact value of each expression. See Example 1. tan 165
 5.4.12: Find the exact value of each expression. See Example 1. tan 285
 5.4.13: Find the exact value of each expression. See Example 1. sin5p12
 5.4.14: Find the exact value of each expression. See Example 1. sin13p12
 5.4.15: Find the exact value of each expression. See Example 1. tan p12
 5.4.16: Find the exact value of each expression. See Example 1. tan 5p12
 5.4.17: Find the exact value of each expression. See Example 1. sin7p12
 5.4.18: Find the exact value of each expression. See Example 1. sin p12
 5.4.19: Find the exact value of each expression. See Example 1. sin a  7p12 b
 5.4.20: Find the exact value of each expression. See Example 1. . sin a  5...
 5.4.21: Find the exact value of each expression. See Example 1. tan a  5p12 b
 5.4.22: Find the exact value of each expression. See Example 1. tan a  7p12 b
 5.4.23: Find the exact value of each expression. See Example 1. tan11p12
 5.4.24: Find the exact value of each expression. See Example 1. sin a  13p...
 5.4.25: Find the exact value of each expression. See Example 1. sin 76 cos ...
 5.4.26: Find the exact value of each expression. See Example 1. sin 40 cos ...
 5.4.27: Find the exact value of each expression. See Example 1. sin p5 cos ...
 5.4.28: Find the exact value of each expression. See Example 1. sin5p9 cos ...
 5.4.29: Find the exact value of each expression. See Example 1. tan 80 + ta...
 5.4.30: Find the exact value of each expression. See Example 1. tan 80  ta...
 5.4.31: Find the exact value of each expression. See Example 1. tan 5p9 + t...
 5.4.32: Find the exact value of each expression. See Example 1. tan 5p12 + ...
 5.4.33: Write each function as an expression involving functions of u or x ...
 5.4.34: Write each function as an expression involving functions of u or x ...
 5.4.35: Write each function as an expression involving functions of u or x ...
 5.4.36: Write each function as an expression involving functions of u or x ...
 5.4.37: Write each function as an expression involving functions of u or x ...
 5.4.38: Write each function as an expression involving functions of u or x ...
 5.4.39: Write each function as an expression involving functions of u or x ...
 5.4.40: Write each function as an expression involving functions of u or x ...
 5.4.41: Write each function as an expression involving functions of u or x ...
 5.4.42: Write each function as an expression involving functions of u or x ...
 5.4.43: Write each function as an expression involving functions of u or x ...
 5.4.44: Write each function as an expression involving functions of u or x ...
 5.4.45: Write each function as an expression involving functions of u or x ...
 5.4.46: Write each function as an expression involving functions of u or x ...
 5.4.47: Write each function as an expression involving functions of u or x ...
 5.4.48: Why is it not possible to use the method of Example 2 to find a for...
 5.4.49: Why is it that standard trigonometry texts usually do not develop f...
 5.4.50: Show that if A, B, and C are the angles of a triangle, then sin1A +...
 5.4.51: Use the given information to find (a) sin1s + t2, (b) tan1s + t2, a...
 5.4.52: Use the given information to find (a) sin1s + t2, (b) tan1s + t2, a...
 5.4.53: Use the given information to find (a) sin1s + t2, (b) tan1s + t2, a...
 5.4.54: Use the given information to find (a) sin1s + t2, (b) tan1s + t2, a...
 5.4.55: Use the given information to find (a) sin1s + t2, (b) tan1s + t2, a...
 5.4.56: Use the given information to find (a) sin1s + t2, (b) tan1s + t2, a...
 5.4.57: Graph each expression and use the graph to make a conjecture, predi...
 5.4.58: Graph each expression and use the graph to make a conjecture, predi...
 5.4.59: Graph each expression and use the graph to make a conjecture, predi...
 5.4.60: Graph each expression and use the graph to make a conjecture, predi...
 5.4.61: Verify that each equation is an identity. See Example 4. sin 2x = 2...
 5.4.62: Verify that each equation is an identity. See Example 4. sin1x + y2...
 5.4.63: Verify that each equation is an identity. See Example 4. sin a7p6+ ...
 5.4.64: Verify that each equation is an identity. See Example 4. tan1x  y2...
 5.4.65: Verify that each equation is an identity. See Example 4. cos1a  b2...
 5.4.66: Verify that each equation is an identity. See Example 4. sin1s + t2...
 5.4.67: Verify that each equation is an identity. See Example 4. sin1x  y2...
 5.4.68: Verify that each equation is an identity. See Example 4. sin1x + y2...
 5.4.69: Verify that each equation is an identity. See Example 4. sin1s  t2...
 5.4.70: Verify that each equation is an identity. See Example 4. tan1a + b2...
 5.4.71: Back Stress If a person bends at the waist with a straight back mak...
 5.4.72: Back Stress Refer to Exercise 71. (a) Suppose a 200lb person bends...
 5.4.73: Voltage A coil of wire rotating in a magnetic field induces a volta...
 5.4.74: Voltage of a Circuit When the two voltages V1 = 30 sin 120pt and V2...
 5.4.75: The figure on the left below shows the three quantities that determ...
 5.4.76: The figure on the left below shows the three quantities that determ...
 5.4.77: For individual or collaborative investigation (Exercises 7782) Refe...
 5.4.78: For individual or collaborative investigation (Exercises 7782) Refe...
 5.4.79: For individual or collaborative investigation (Exercises 7782) Refe...
 5.4.80: For individual or collaborative investigation (Exercises 7782) Refe...
 5.4.81: Use the result from Exercise 80 to find the acute angle between eac...
 5.4.82: Use the result from Exercise 80 to find the acute angle between eac...
Solutions for Chapter 5.4: Sum and Difference Identities for Sine and Tangent
Full solutions for Trigonometry  11th Edition
ISBN: 9780134217437
Solutions for Chapter 5.4: Sum and Difference Identities for Sine and Tangent
Get Full SolutionsSince 82 problems in chapter 5.4: Sum and Difference Identities for Sine and Tangent have been answered, more than 25975 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Trigonometry, edition: 11. Trigonometry was written by and is associated to the ISBN: 9780134217437. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.4: Sum and Difference Identities for Sine and Tangent includes 82 full stepbystep solutions.

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.

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib IIĀ· Condition numbers measure the sensitivity of the output to change in the input.

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

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

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

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

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

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

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

Left inverse A+.
If A has full column rank n, then A+ = (AT A)I AT has A+ A = In.

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

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

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

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

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.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.