 6.4.1: Which one of the following equations has solution 0? A. arctan 1 = ...
 6.4.2: Which one of the following equations has solution p4 ? A. arcsin 22...
 6.4.3: Which one of the following equations has solution 3p 4 ? A. arctan ...
 6.4.4: Which one of the following equations has solution  p6 ? A. arctan ...
 6.4.5: Solve each equation for x, where x is restricted to the given inter...
 6.4.6: Solve each equation for x, where x is restricted to the given inter...
 6.4.7: Solve each equation for x, where x is restricted to the given inter...
 6.4.8: Solve each equation for x, where x is restricted to the given inter...
 6.4.9: Solve each equation for x, where x is restricted to the given inter...
 6.4.10: Solve each equation for x, where x is restricted to the given inter...
 6.4.11: Solve each equation for x, where x is restricted to the given inter...
 6.4.12: Solve each equation for x, where x is restricted to the given inter...
 6.4.13: Solve each equation for x, where x is restricted to the given inter...
 6.4.14: Solve each equation for x, where x is restricted to the given inter...
 6.4.15: Solve each equation for x, where x is restricted to the given inter...
 6.4.16: Solve each equation for x, where x is restricted to the given inter...
 6.4.17: Solve each equation for x, where x is restricted to the given inter...
 6.4.18: Solve each equation for x, where x is restricted to the given inter...
 6.4.19: Solve each equation for x, where x is restricted to the given inter...
 6.4.20: Solve each equation for x, where x is restricted to the given inter...
 6.4.21: Solve each equation for x, where x is restricted to the given inter...
 6.4.22: Solve each equation for x, where x is restricted to the given inter...
 6.4.23: Refer to Exercise 17. A student attempting to solve this equation w...
 6.4.24: Explain why the equation sin1 x = cos1 2 cannot have a solution. ...
 6.4.25: Solve each equation for exact solutions. See Examples 2 and 3. 4 a...
 6.4.26: Solve each equation for exact solutions. See Examples 2 and 3. 6 ar...
 6.4.27: Solve each equation for exact solutions. See Examples 2 and 3. 4 3 ...
 6.4.28: Solve each equation for exact solutions. See Examples 2 and 3. 4p +...
 6.4.29: Solve each equation for exact solutions. See Examples 2 and 3. 2 ar...
 6.4.30: Solve each equation for exact solutions. See Examples 2 and 3. arcc...
 6.4.31: Solve each equation for exact solutions. See Examples 2 and 3. arcs...
 6.4.32: Solve each equation for exact solutions. See Examples 2 and 3. arct...
 6.4.33: Solve each equation for exact solutions. See Examples 2 and 3. cos...
 6.4.34: Solve each equation for exact solutions. See Examples 2 and 3. cot...
 6.4.35: Solve each equation for exact solutions. See Example 4. sin1 x  t...
 6.4.36: Solve each equation for exact solutions. See Example 4. sin1 x + t...
 6.4.37: Solve each equation for exact solutions. See Example 4. arccos x + ...
 6.4.38: Solve each equation for exact solutions. See Example 4. arccos x + ...
 6.4.39: Solve each equation for exact solutions. See Example 4. arcsin 2x +...
 6.4.40: Solve each equation for exact solutions. See Example 4. arcsin 2x +...
 6.4.41: Solve each equation for exact solutions. See Example 4. cos1 x + t...
 6.4.42: Solve each equation for exact solutions. See Example 4. sin1 x + t...
 6.4.43: Provide graphical support for the solution in Example 4 by showing ...
 6.4.44: Provide graphical support for the solution in Example 4 by showing ...
 6.4.45: The following equations cannot be solved by algebraic methods. Use ...
 6.4.46: The following equations cannot be solved by algebraic methods. Use ...
 6.4.47: Tone Heard by a Listener When two sources located at different posi...
 6.4.48: Tone Heard by a Listener Repeat Exercise 47. Use A1 = 0.0025, f1 = ...
 6.4.49: Depth of Field When a largeview camera is used to take a picture o...
 6.4.50: Programming Language for Inverse Functions In Visual Basic, a widel...
 6.4.51: Alternating Electric Current In the study of alternating electric c...
 6.4.52: Viewing Angle of an Observer While visiting a museum, Marsha Langlo...
 6.4.53: Movement of an Arm In the equation below, t is time (in seconds) an...
 6.4.54: The function y = sec1 x is not found on graphing calculators. Howe...
Solutions for Chapter 6.4: Equations Involving Inverse Trigonometric Functions
Full solutions for Trigonometry  10th Edition
ISBN: 9780321671776
Solutions for Chapter 6.4: Equations Involving Inverse Trigonometric Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 54 problems in chapter 6.4: Equations Involving Inverse Trigonometric Functions have been answered, more than 34243 students have viewed full stepbystep solutions from this chapter. Trigonometry was written by and is associated to the ISBN: 9780321671776. Chapter 6.4: Equations Involving Inverse Trigonometric Functions includes 54 full stepbystep solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: 10.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Exponential eAt = I + At + (At)2 12! + ...
has derivative AeAt; eAt u(O) solves u' = Au.

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!).

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

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.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

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

Matrix multiplication AB.
The i, j entry of AB is (row i of A)·(column j of B) = L aikbkj. By columns: Column j of AB = A times column j of B. By rows: row i of A multiplies B. Columns times rows: AB = sum of (column k)(row k). All these equivalent definitions come from the rule that A B times x equals A times B x .

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

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

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

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

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

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!

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

Toeplitz matrix.
Constant down each diagonal = timeinvariant (shiftinvariant) filter.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.