 5.4.1: Concept Check Match each expression in Column I with its value in C...
 5.4.2: Concept Check Match each expression in Column I with its value in C...
 5.4.3: Concept Check Match each expression in Column I with its value in C...
 5.4.4: Concept Check Match each expression in Column I with its value in C...
 5.4.5: Concept Check Match each expression in Column I with its value in C...
 5.4.6: Concept Check Match each expression in Column I with its value in C...
 5.4.7: Compare the formulas for sin1A  B2 and sin1A + B2. How do they dif...
 5.4.8: Compare the formulas for tan1A  B2 and tan1A + B2. How do they dif...
 5.4.9: Use identities to find each exact value. See Example 1. sin 5p 12
 5.4.10: Use identities to find each exact value. See Example 1. sin 13p 12
 5.4.11: Use identities to find each exact value. See Example 1. tan p 12
 5.4.12: Use identities to find each exact value. See Example 1. tan 5p 12
 5.4.13: Use identities to find each exact value. See Example 1. sin 7p 12
 5.4.14: Use identities to find each exact value. See Example 1. sin p 12
 5.4.15: Use identities to find each exact value. See Example 1. sin a 7p 12 b
 5.4.16: Use identities to find each exact value. See Example 1. sin a 5p 12 b
 5.4.17: Use identities to find each exact value. See Example 1. tan a 5p 12 b
 5.4.18: Use identities to find each exact value. See Example 1. tan a 7p 12 B
 5.4.19: Use identities to find each exact value. See Example 1. sin 76_ cos...
 5.4.20: Use identities to find each exact value. See Example 1. sin 40_ cos...
 5.4.21: Use identities to find each exact value. See Example 1. tan 80_ + t...
 5.4.22: Use identities to find each exact value. See Example 1. tan 80_  t...
 5.4.23: Use identities to find each exact value. See Example 1. tan 100_ + ...
 5.4.24: Use identities to find each exact value. See Example 1. tan 5p 12 +...
 5.4.25: Use identities to find each exact value. See Example 1. sin p 5 cos...
 5.4.26: Use identities to find each exact value. See Example 1. sin 100_ co...
 5.4.27: Use identities to write each expression as a single function of x o...
 5.4.28: Use identities to write each expression as a single function of x o...
 5.4.29: Use identities to write each expression as a single function of x o...
 5.4.30: Use identities to write each expression as a single function of x o...
 5.4.31: Use identities to write each expression as a single function of x o...
 5.4.32: Use identities to write each expression as a single function of x o...
 5.4.33: Use identities to write each expression as a single function of x o...
 5.4.34: Use identities to write each expression as a single function of x o...
 5.4.35: Use identities to write each expression as a single function of x o...
 5.4.36: Use identities to write each expression as a single function of x o...
 5.4.37: Use identities to write each expression as a single function of x o...
 5.4.38: Use identities to write each expression as a single function of x o...
 5.4.39: Use identities to write each expression as a single function of x o...
 5.4.40: Use identities to write each expression as a single function of x o...
 5.4.41: Use identities to write each expression as a single function of x o...
 5.4.42: Why is it not possible to use the method of Example 2 to find a for...
 5.4.43: Why is it that standard trigonometry texts usually do not develop f...
 5.4.44: Show that if A, B, and C are the angles of a triangle, then sin1A +...
 5.4.45: Use the given information to find (a) sin1s + t2, (b) tan1s + t2, a...
 5.4.46: Use the given information to find (a) sin1s + t2, (b) tan1s + t2, a...
 5.4.47: Use the given information to find (a) sin1s + t2, (b) tan1s + t2, a...
 5.4.48: Use the given information to find (a) sin1s + t2, (b) tan1s + t2, a...
 5.4.49: Use the given information to find (a) sin1s + t2, (b) tan1s + t2, a...
 5.4.50: Use the given information to find (a) sin1s + t2, (b) tan1s + t2, a...
 5.4.51: Find each exact value. Use an appropriate sum or difference identit...
 5.4.52: Find each exact value. Use an appropriate sum or difference identit...
 5.4.53: Find each exact value. Use an appropriate sum or difference identit...
 5.4.54: Find each exact value. Use an appropriate sum or difference identit...
 5.4.55: Find each exact value. Use an appropriate sum or difference identit...
 5.4.56: Find each exact value. Use an appropriate sum or difference identit...
 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 a 7p 6...
 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: In terms of b, what is the measure of angle ABC ?
 5.4.72: Use the fact that the sum of the angles in a triangle is 180_ to ex...
 5.4.73: Apply the formula for tan1A  B2 to obtain an expression for tan u ...
 5.4.74: Replace tan a with m1 and tan b with m2 to obtain tan u = m2  m1 1...
 5.4.75: In Exercises 75 and 76, use the result from Exercise 74 to find the...
 5.4.76: In Exercises 75 and 76, use the result from Exercise 74 to find the...
 5.4.77: Back Stress If a person bends at the waist with a straight back mak...
 5.4.78: Back Stress Refer to Exercise 77. (a) Suppose a 200lb person bends...
 5.4.79: Voltage A coil of wire rotating in a magnetic field induces a volta...
 5.4.80: Voltage of a Circuit When the two voltages V1 = 30 sin 120pt and V2...
 5.4.81: Write y_ in terms of y, R, and z.
 5.4.82: Write z_ in terms of y, R, and z.
Solutions for Chapter 5.4: Sum and Difference Identities for Sine and Tangent
Full solutions for Trigonometry  10th Edition
ISBN: 9780321671776
Solutions for Chapter 5.4: Sum and Difference Identities for Sine and Tangent
Get Full SolutionsThis textbook survival guide was created for the textbook: Trigonometry, edition: 10. Since 82 problems in chapter 5.4: Sum and Difference Identities for Sine and Tangent have been answered, more than 32661 students have viewed full stepbystep solutions from this chapter. Trigonometry was written by and is associated to the ISBN: 9780321671776. 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.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

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.

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

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

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Jordan form 1 = M 1 AM.
If A has s independent eigenvectors, its "generalized" eigenvector matrix M gives 1 = diag(lt, ... , 1s). The block his Akh +Nk where Nk has 1 's on diagonall. Each block has one eigenvalue Ak and one eigenvector.

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

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

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

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

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.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

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

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

Vector v in Rn.
Sequence of n real numbers v = (VI, ... , Vn) = point in Rn.