 5.6.1: Determine whether the positive or negative square root should be se...
 5.6.2: Determine whether the positive or negative square root should be se...
 5.6.3: Determine whether the positive or negative square root should be se...
 5.6.4: Determine whether the positive or negative square root should be se...
 5.6.5: Match each expression in Column I with its value in Column II. sin ...
 5.6.6: Match each expression in Column I with its value in Column II. tan ...
 5.6.7: Match each expression in Column I with its value in Column II. cos ...
 5.6.8: Match each expression in Column I with its value in Column II. tan ...
 5.6.9: Match each expression in Column I with its value in Column II. tan ...
 5.6.10: Match each expression in Column I with its value in Column II. cos ...
 5.6.11: Use a halfangle identity to find each exact value. See Examples 1 ...
 5.6.12: Use a halfangle identity to find each exact value. See Examples 1 ...
 5.6.13: Use a halfangle identity to find each exact value. See Examples 1 ...
 5.6.14: Use a halfangle identity to find each exact value. See Examples 1 ...
 5.6.15: Use a halfangle identity to find each exact value. See Examples 1 ...
 5.6.16: Use a halfangle identity to find each exact value. See Examples 1 ...
 5.6.17: Explain how to use identities from this section to find the exact v...
 5.6.18: The halfangle identity tan A 2 = {B 1  cos A 1 + cos A can be use...
 5.6.19: Use the given information to find each of the following. See Exampl...
 5.6.20: Use the given information to find each of the following. See Exampl...
 5.6.21: Use the given information to find each of the following. See Exampl...
 5.6.22: Use the given information to find each of the following. See Exampl...
 5.6.23: Use the given information to find each of the following. See Exampl...
 5.6.24: Use the given information to find each of the following. See Exampl...
 5.6.25: Use the given information to find each of the following. See Exampl...
 5.6.26: Use the given information to find each of the following. See Exampl...
 5.6.27: Use the given information to find each of the following. See Exampl...
 5.6.28: Use the given information to find each of the following. See Exampl...
 5.6.29: Use the given information to find each of the following. See Exampl...
 5.6.30: Use the given information to find each of the following. See Exampl...
 5.6.31: Concept Check If cos x 0.9682 and sin x = 0.250, then tan x 2 .
 5.6.32: Concept Check If cos x = 0.750 and sin x 0.6614, then tan x 2 .
 5.6.33: Simplify each expression. See Example 4. B 1  cos 40 2
 5.6.34: Simplify each expression. See Example 4. B 1 + cos 76 2
 5.6.35: Simplify each expression. See Example 4. B 1  cos 147 1 + cos 147
 5.6.36: Simplify each expression. See Example 4. B 1 + cos 165 1  cos 165
 5.6.37: Simplify each expression. See Example 4. 1  cos 59.74 sin 59.74
 5.6.38: Simplify each expression. See Example 4. sin 158.2 1 + cos 158.2
 5.6.39: Simplify each expression. See Example 4. {B 1 + cos 18x 2
 5.6.40: Simplify each expression. See Example 4. {B 1 + cos 20a 2
 5.6.41: Simplify each expression. See Example 4. {B 1  cos 8u 1 + cos 8u
 5.6.42: Simplify each expression. See Example 4. {B 1  cos 5A 1 + cos 5A
 5.6.43: Simplify each expression. See Example 4. {B 1 + cos x 4 2
 5.6.44: Simplify each expression. See Example 4. { D 1  cos 3u 5 2
 5.6.45: Verify that each equation is an identity. See Example 5. sec2 x 2 =...
 5.6.46: Verify that each equation is an identity. See Example 5. cot2 x 2 =...
 5.6.47: Verify that each equation is an identity. See Example 5. sin2 x 2 =...
 5.6.48: Verify that each equation is an identity. See Example 5. sin 2x 2 s...
 5.6.49: Verify that each equation is an identity. See Example 5. 2 1 + cos ...
 5.6.50: Verify that each equation is an identity. See Example 5. tan u 2 = ...
 5.6.51: Verify that each equation is an identity. See Example 5. 1  tan2 u...
 5.6.52: Verify that each equation is an identity. See Example 5. cos x = 1 ...
 5.6.53: Use the halfangle identity tan A 2 = sin A 1 + cos A to derive the...
 5.6.54: Use the identity tan A 2 = sin A 1 + cos A to determine an identity...
 5.6.55: Graph each expression and use the graph to make a conjecture, predi...
 5.6.56: Graph each expression and use the graph to make a conjecture, predi...
 5.6.57: Graph each expression and use the graph to make a conjecture, predi...
 5.6.58: Graph each expression and use the graph to make a conjecture, predi...
 5.6.59: An airplane flying faster than the speed of sound sends out sound w...
 5.6.60: An airplane flying faster than the speed of sound sends out sound w...
 5.6.61: An airplane flying faster than the speed of sound sends out sound w...
 5.6.62: An airplane flying faster than the speed of sound sends out sound w...
 5.6.63: (Modeling) Railroad Curves In the United States, circular railroad ...
 5.6.64: In Exercise 63, if b = 12, what is the measure of angle u to the ne...
 5.6.65: (See Hobsons A Treatise on Plane Trigonometry.) Use this value and ...
 5.6.66: (See Hobsons A Treatise on Plane Trigonometry.) Use this value and ...
 5.6.67: (See Hobsons A Treatise on Plane Trigonometry.) Use this value and ...
 5.6.68: (See Hobsons A Treatise on Plane Trigonometry.) Use this value and ...
 5.6.69: (See Hobsons A Treatise on Plane Trigonometry.) Use this value and ...
 5.6.70: (See Hobsons A Treatise on Plane Trigonometry.) Use this value and ...
 5.6.71: (See Hobsons A Treatise on Plane Trigonometry.) Use this value and ...
 5.6.72: (See Hobsons A Treatise on Plane Trigonometry.) Use this value and ...
 5.6.73: (See Hobsons A Treatise on Plane Trigonometry.) Use this value and ...
 5.6.74: (See Hobsons A Treatise on Plane Trigonometry.) Use this value and ...
 5.6.75: (See Hobsons A Treatise on Plane Trigonometry.) Use this value and ...
 5.6.76: (See Hobsons A Treatise on Plane Trigonometry.) Use this value and ...
 5.6.77: These exercises use results from plane geometry to obtain exact val...
 5.6.78: These exercises use results from plane geometry to obtain exact val...
 5.6.79: These exercises use results from plane geometry to obtain exact val...
 5.6.80: These exercises use results from plane geometry to obtain exact val...
 5.6.81: These exercises use results from plane geometry to obtain exact val...
 5.6.82: These exercises use results from plane geometry to obtain exact val...
 5.6.83: These exercises use results from plane geometry to obtain exact val...
 5.6.84: These exercises use results from plane geometry to obtain exact val...
Solutions for Chapter 5.6: HalfAngle Identities
Full solutions for Trigonometry  11th Edition
ISBN: 9780134217437
Solutions for Chapter 5.6: HalfAngle Identities
Get Full SolutionsThis textbook survival guide was created for the textbook: Trigonometry, edition: 11. Trigonometry was written by and is associated to the ISBN: 9780134217437. Since 84 problems in chapter 5.6: HalfAngle Identities have been answered, more than 10421 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.6: HalfAngle Identities includes 84 full stepbystep solutions.

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.)

Commuting matrices AB = BA.
If diagonalizable, they share n eigenvectors.

Conjugate Gradient Method.
A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax  x Tb over growing Krylov subspaces.

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].

Diagonalizable matrix A.
Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then SI AS = A = eigenvalue matrix.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

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.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

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.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

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).

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.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Random matrix rand(n) or randn(n).
MATLAB creates a matrix with random entries, uniformly distributed on [0 1] for rand and standard normal distribution for randn.

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

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector space V.
Set of vectors such that all combinations cv + d w remain within V. Eight required rules are given in Section 3.1 for scalars c, d and vectors v, w.
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