 6.1: Graph the inverse sine, cosine, and tangent functions, indicating t...
 6.2: The ranges of the inverse tangent and inverse cotangent functions a...
 6.3: It is true that sin 11p6 =  12, and therefore arcsin A  12B = 11p6 .
 6.4: For all x, tan1tan1 x2 = x.
 6.5: Find the exact value of each real number y. Do not use a calculator...
 6.6: Find the exact value of each real number y. Do not use a calculator...
 6.7: Find the exact value of each real number y. Do not use a calculator...
 6.8: Find the exact value of each real number y. Do not use a calculator...
 6.9: Find the exact value of each real number y. Do not use a calculator...
 6.10: Find the exact value of each real number y. Do not use a calculator...
 6.11: Find the exact value of each real number y. Do not use a calculator...
 6.12: Find the exact value of each real number y. Do not use a calculator...
 6.13: Find the exact value of each real number y. Do not use a calculator...
 6.14: Give the degree measure of u. Do not use a calculator. u = arccos12
 6.15: Give the degree measure of u. Do not use a calculator. u = arcsin 232
 6.16: Give the degree measure of u. Do not use a calculator. u = tan1 0
 6.17: Use a calculator to approximate each value in decimal degrees u = a...
 6.18: Use a calculator to approximate each value in decimal degrees u = s...
 6.19: Use a calculator to approximate each value in decimal degrees u = c...
 6.20: Use a calculator to approximate each value in decimal degrees u = c...
 6.21: Use a calculator to approximate each value in decimal degrees u = a...
 6.22: Use a calculator to approximate each value in decimal degrees u = c...
 6.23: Evaluate each expression without using a calculator. cos1arccos1122
 6.24: Evaluate each expression without using a calculator. sin arcsin 2322
 6.25: Evaluate each expression without using a calculator.arccos acos3p4b
 6.26: Evaluate each expression without using a calculator.arcsec1sec p2
 6.27: Evaluate each expression without using a calculator.tan1 atanp4b
 6.28: Evaluate each expression without using a calculator.cos11cos 02
 6.29: Evaluate each expression without using a calculator.sin aarccos34b
 6.30: Evaluate each expression without using a calculator.cos1arctan 32
 6.31: Evaluate each expression without using a calculator.cos1csc1122
 6.32: Evaluate each expression without using a calculator.sec a2 sin1 a...
 6.33: Evaluate each expression without using a calculator.tan aarcsin35 +...
 6.34: Write each trigonometric expression as an algebraic expression in u...
 6.35: Write each trigonometric expression as an algebraic expression in u...
 6.36: Solve each equation for exact solutions over the interval 30, 2p2 w...
 6.37: Solve each equation for exact solutions over the interval 30, 2p2 w...
 6.38: Solve each equation for exact solutions over the interval 30, 2p2 w...
 6.39: Solve each equation for exact solutions over the interval 30, 2p2 w...
 6.40: Solve each equation for exact solutions over the interval 30, 2p2 w...
 6.41: Solve each equation for exact solutions over the interval 30, 2p2 w...
 6.42: Solve each equation for all exact solutions, in radians. secx2 = cosx2
 6.43: Solve each equation for all exact solutions, in radians. cos 2x + c...
 6.44: Solve each equation for all exact solutions, in radians. 4 sin x co...
 6.45: Solve each equation for exact solutions over the interval 30 3602 w...
 6.46: Solve each equation for exact solutions over the interval 30 3602 w...
 6.47: Solve each equation for exact solutions over the interval 30 3602 w...
 6.48: Solve each equation for exact solutions over the interval 30 3602 w...
 6.49: Solve each equation for exact solutions over the interval 30 3602 w...
 6.50: Solve each equation for exact solutions over the interval 30 3602 w...
 6.51: Solve each equation for all exact solutions, in degrees. 223 cosu2 ...
 6.52: Solve each equation for all exact solutions, in degrees. sin u  co...
 6.53: Solve each equation for all exact solutions, in degrees. tan u  se...
 6.54: Solve each equation for x. 4p  4 cot1 x = p
 6.55: Solve each equation for x. 43arctanx2 = p
 6.56: Solve each equation for x. arccos x = arcsin27
 6.57: Solve each equation for x. arccos x + arctan 1 =11p12
 6.58: Solve each equation for x. y = 3 cosx2, for x in 30, 2p4
 6.59: Solve each equation for x. y =12sin x, for x in c p2,p2d
 6.60: Solve each equation for x. y =45sin x 35, for x in c p2,p2d
 6.61: Solve each equation for x. y =12tan13x + 22, for x in a23  p6, 2...
 6.62: Solve each equation for x. Solve d = 550 + 450 cos a p50tb for t, w...
 6.63: Viewing Angle of an Observer A 10ftwide chalkboardis situated 5 f...
 6.64: Snells Law Snells law states thatc1c2=sin u1sin u2,where c1 is the ...
 6.65: Snells Law Refer to Exercise 64. What happens when u1 is greater th...
 6.66: British Nautical Mile The British nauticalmile is defined as the le...
Solutions for Chapter 6: Inverse Circular Functions and Trigonometric Equations
Full solutions for Trigonometry  11th Edition
ISBN: 9780134217437
Solutions for Chapter 6: Inverse Circular Functions and Trigonometric Equations
Get Full SolutionsThis textbook survival guide was created for the textbook: Trigonometry, edition: 11. Since 66 problems in chapter 6: Inverse Circular Functions and Trigonometric Equations have been answered, more than 60758 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Trigonometry was written by and is associated to the ISBN: 9780134217437. Chapter 6: Inverse Circular Functions and Trigonometric Equations includes 66 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.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

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.

Cofactor Cij.
Remove row i and column j; multiply the determinant by (I)i + j •

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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].

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

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

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.

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

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.

lAII = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n  1, volume of box = I det( A) I.

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.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

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

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

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.