 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 9657 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.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

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.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

Column space C (A) =
space of all combinations of the columns 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 IIĀ· Condition numbers measure the sensitivity of the output to change in the input.

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

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

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

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!).

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

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Minimal polynomial of A.
The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A  AI) if no eigenvalues are repeated; always meA) divides peA).

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Partial pivoting.
In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(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.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.
I don't want to reset my password
Need help? Contact support
Having trouble accessing your account? Let us help you, contact support at +1(510) 9441054 or support@studysoup.com
Forgot password? Reset it here