 2.2.2.1.74: Add or subtract as indicated. (37 45') + (26 24')
 2.2.2.1.75: Add or subtract as indicated. (37 45') + (26 24')
 2.2.2.1.76: Add or subtract as indicated. (51055') + (37 45')
 2.2.2.1.77: Add or subtract as indicated. (63 38') + (24 52')
 2.2.2.1.78: Add or subtract as indicated. (61 33') + (45 16')
 2.2.2.1.79: Add or subtract as indicated. (7721') + (230 16')
 2.2.2.1.80: Add or subtract as indicated. 90  (34 12')
 2.2.2.1.81: Add or subtract as indicated. 90  (62 25')
 2.2.2.1.82: Add or subtract as indicated. 180  (120 17')
 2.2.2.1.83: Add or subtract as indicated. 180  (112 19')
 2.2.2.1.84: Add or subtract as indicated. (76 24')  (22 34')
 2.2.2.1.85: Add or subtract as indicated. (89 38')  (28 58')
 2.2.2.1.86: Add or subtract as indicated. (70 40')  (30 SO')
 2.2.2.1.87: Add or subtract as indicated. (80 SO')  (500 56')
 2.2.2.1.88: Convert each of the following to degrees and minutes.35.4
 2.2.2.1.89: Convert each of the following to degrees and minutes.63.2
 2.2.2.1.90: Convert each of the following to degrees and minutes.16.25
 2.2.2.1.91: Convert each of the following to degrees and minutes.18.75
 2.2.2.1.92: Convert each of the following to degrees and minutes.92.55
 2.2.2.1.93: Convert each of the following to degrees and minutes.34.45
 2.2.2.1.94: Convert each of the following to degrees and minutes.19.9
 2.2.2.1.95: Convert each of the following to degrees and minutes.18.8
 2.2.2.1.96: Change each of the following to decimal degrees. If rounding is nec...
 2.2.2.1.97: Change each of the following to decimal degrees. If rounding is nec...
 2.2.2.1.98: Change each of the following to decimal degrees. If rounding is nec...
 2.2.2.1.99: Change each of the following to decimal degrees. If rounding is nec...
 2.2.2.1.100: Change each of the following to decimal degrees. If rounding is nec...
 2.2.2.1.101: Change each of the following to decimal degrees. If rounding is nec...
 2.2.2.1.102: Change each of the following to decimal degrees. If rounding is nec...
 2.2.2.1.103: Change each of the following to decimal degrees. If rounding is nec...
 2.2.2.1.104: Use a calculator to find each of the following. Round all answers t...
 2.2.2.1.105: Use a calculator to find each of the following. Round all answers t...
 2.2.2.1.106: Use a calculator to find each of the following. Round all answers t...
 2.2.2.1.107: Use a calculator to find each of the following. Round all answers t...
 2.2.2.1.108: Use a calculator to find each of the following. Round all answers t...
 2.2.2.1.109: Use a calculator to find each of the following. Round all answers t...
 2.2.2.1.110: Use a calculator to find each of the following. Round all answers t...
 2.2.2.1.111: Use a calculator to find each of the following. Round all answers t...
 2.2.2.1.112: Use a calculator to find each of the following. Round all answers t...
 2.2.2.1.113: Use a calculator to find each of the following. Round all answers t...
 2.2.2.1.114: Use a calculator to find each of the following. Round all answers t...
 2.2.2.1.115: Use a calculator to find each of the following. Round all answers t...
 2.2.2.1.116: Use a calcu1ato~ to find each of the fol1owing. Round all answers t...
 2.2.2.1.117: Use a calcu1ato~ to find each of the fol1owing. Round all answers t...
 2.2.2.1.118: Use a calcu1ato~ to find each of the fol1owing. Round all answers t...
 2.2.2.1.119: Use a calcu1ato~ to find each of the fol1owing. Round all answers t...
 2.2.2.1.120: Use a calcu1ato~ to find each of the fol1owing. Round all answers t...
 2.2.2.1.121: Use a calcu1ato~ to find each of the fol1owing. Round all answers t...
 2.2.2.1.122: Use a calcu1ato~ to find each of the fol1owing. Round all answers t...
 2.2.2.1.123: Use a calcu1ato~ to find each of the fol1owing. Round all answers t...
 2.2.2.1.124: Use a calculator to complete the following tables. (Be sure your ca...
 2.2.2.1.125: Use a calculator to complete the following tables. (Be sure your ca...
 2.2.2.1.126: Use a calculator to complete the fol1owing tables. (Be sure your ca...
 2.2.2.1.127: Use a calculator to complete the fol1owing tables. (Be sure your ca...
 2.2.2.1.128: Find (J if (J is between 0 and 90. Round your answers to the neares...
 2.2.2.1.129: Find (J if (J is between 0 and 90. Round your answers to the neares...
 2.2.2.1.130: Find (J if (J is between 0 and 90. Round your answers to the neares...
 2.2.2.1.131: Find (J if (J is between 0 and 90. Round your answers to the neares...
 2.2.2.1.132: Find (J if (J is between 0 and 90. Round your answers to the neares...
 2.2.2.1.133: Find (J if (J is between 0 and 90. Round your answers to the neares...
 2.2.2.1.134: Find (J if (J is between 0 and 90. Round your answers to the neares...
 2.2.2.1.135: Find (J if (J is between 0 and 90. Round your answers to the neares...
 2.2.2.1.136: Find (J if (J is between 0 and 90. Round your answers to the neares...
 2.2.2.1.137: Find (J if (J is between 0 and 90. Round your answers to the neares...
 2.2.2.1.138: Find (J if (J is between 0 and 90. Round your answers to the neares...
 2.2.2.1.139: Find (J if (J is between 0 and 90. Round your answers to the neares...
 2.2.2.1.140: Use a calculator to find a value of (J between 0" and 90 that satis...
 2.2.2.1.141: Use a calculator to find a value of (J between 0" and 90 that satis...
 2.2.2.1.142: Use a calculator to find a value of (J between 0" and 90 that satis...
 2.2.2.1.143: Use a calculator to find a value of (J between 0" and 90 that satis...
 2.2.2.1.144: Use a calculator to find a value of (J between 0" and 90 that satis...
 2.2.2.1.145: Use a calculator to find a value of (J between 0" and 90 that satis...
 2.2.2.1.146: Use a calculator to find a value of (J between 0" and 90 that satis...
 2.2.2.1.147: Use a calculator to find a value of (J between 0" and 90 that satis...
 2.2.2.1.148: To further justify the Cofunction Theorem, use your calculator to f...
 2.2.2.1.149: To further justify the Cofunction Theorem, use your calculator to f...
 2.2.2.1.150: To further justify the Cofunction Theorem, use your calculator to f...
 2.2.2.1.151: To further justify the Cofunction Theorem, use your calculator to f...
 2.2.2.1.152: To further justify the Cofunction Theorem, use your calculator to f...
 2.2.2.1.153: To further justify the Cofunction Theorem, use your calculator to f...
 2.2.2.1.154: Work each of the following problems on your calculator. Do not writ...
 2.2.2.1.155: Work each of the following problems on your calculator. Do not writ...
 2.2.2.1.156: Work each of the following problems on your calculator. Do not writ...
 2.2.2.1.157: Work each of the following problems on your calculator. Do not writ...
 2.2.2.1.158: What happens when you try to find A for sin A = 1.234 on your calcu...
 2.2.2.1.159: What happens when you try to find B for sin B 4.321 on your calcula...
 2.2.2.1.160: What happens when you try to find tan 90 on your calculator? Why do...
 2.2.2.1.161: What happens when you try to find cot 0 on your calculator? Why doe...
 2.2.2.1.162: Complete each of the following tables. Round all answers to the nea...
 2.2.2.1.163: Complete each of the following tables. Round all answers to the nea...
 2.2.2.1.164: Sundials The Moorish sundial is designed so that the shadow of the ...
 2.2.2.1.165: Sundials The Moorish sundial is designed so that the shadow of the ...
 2.2.2.1.166: The problems that follow review material we covered in Section 1.3....
 2.2.2.1.167: The problems that follow review material we covered in Section 1.3....
 2.2.2.1.168: Find sin 8, cos 8, and tan 8 for each value of 8. (Do not use calcu...
 2.2.2.1.169: Find sin 8, cos 8, and tan 8 for each value of 8. (Do not use calcu...
 2.2.2.1.170: Find the remaining trigonometric functions of 8 if cos 8 = 5/13 an...
 2.2.2.1.171: Find the remaining trigonometric functions of 8 if tan 8 =  3/4 an...
 2.2.2.1.172: In which quadrant must the terminal side of 8 lie if sin 8> 0 and c...
 2.2.2.1.173: In which quadrant must the terminal side of 8 lie if tan 8> 0 and s...
Solutions for Chapter 2.2: Right Triangle Trigonometry
Full solutions for Trigonometry
ISBN: 9780495108351
Solutions for Chapter 2.2: Right Triangle Trigonometry
Get Full SolutionsSince 100 problems in chapter 2.2: Right Triangle Trigonometry have been answered, more than 33826 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Trigonometry, edition: . Chapter 2.2: Right Triangle Trigonometry includes 100 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. Trigonometry was written by and is associated to the ISBN: 9780495108351.

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.

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.

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.)

Characteristic equation det(A  AI) = O.
The n roots are the eigenvalues of A.

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 II· Condition numbers measure the sensitivity of the output to change in the input.

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Factorization
A = L U. If elimination takes A to U without row exchanges, then the lower triangular L with multipliers eij (and eii = 1) brings U back to A.

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

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

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.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

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

Least squares solution X.
The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b  Ax is orthogonal to all columns of A.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Normal equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

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.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.