 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 10526 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.

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

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

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

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!).

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.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

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

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.

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

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

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

Positive definite matrix A.
Symmetric matrix with positive eigenvalues and positive pivots. Definition: x T Ax > 0 unless x = O. Then A = LDLT with diag(D» O.

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.

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

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

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

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

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·