 7.1.1: Exer. 150: Verify the identity.csc sin cot cos
 7.1.2: Exer. 150: Verify the identity.sin x cos x cot x csc x
 7.1.3: Exer. 150: Verify the identity.
 7.1.4: Exer. 150: Verify the identity.tan t 2 cos t csc t sec t csc t cot t
 7.1.5: Exer. 150: Verify the identity.
 7.1.6: Exer. 150: Verify the identity.
 7.1.7: Exer. 150: Verify the identity.
 7.1.8: Exer. 150: Verify the identity.
 7.1.9: Exer. 150: Verify the identity.
 7.1.10: Exer. 150: Verify the identity.
 7.1.11: Exer. 150: Verify the identity.
 7.1.12: Exer. 150: Verify the identity.
 7.1.13: Exer. 150: Verify the identity.
 7.1.14: Exer. 150: Verify the identity.
 7.1.15: Exer. 150: Verify the identity.
 7.1.16: Exer. 150: Verify the identity.
 7.1.17: Exer. 150: Verify the identity.
 7.1.18: Exer. 150: Verify the identity.
 7.1.19: Exer. 150: Verify the identity.
 7.1.20: Exer. 150: Verify the identity.
 7.1.21: Exer. 150: Verify the identity.
 7.1.22: Exer. 150: Verify the identity.
 7.1.23: Exer. 150: Verify the identity.
 7.1.24: Exer. 150: Verify the identity.
 7.1.25: Exer. 150: Verify the identity.
 7.1.26: Exer. 150: Verify the identity.
 7.1.27: Exer. 150: Verify the identity.
 7.1.28: Exer. 150: Verify the identity.
 7.1.29: Exer. 150: Verify the identity.
 7.1.30: Exer. 150: Verify the identity.
 7.1.31: Exer. 150: Verify the identity.
 7.1.32: Exer. 150: Verify the identity.
 7.1.33: Exer. 150: Verify the identity.
 7.1.34: Exer. 150: Verify the identity.
 7.1.35: Exer. 150: Verify the identity.
 7.1.36: Exer. 150: Verify the identity.
 7.1.37: Exer. 150: Verify the identity.
 7.1.38: Exer. 150: Verify the identity.
 7.1.39: Exer. 150: Verify the identity.
 7.1.40: Exer. 150: Verify the identity.
 7.1.41: Exer. 150: Verify the identity.
 7.1.42: Exer. 150: Verify the identity.
 7.1.43: Exer. 150: Verify the identity.
 7.1.44: Exer. 150: Verify the identity.
 7.1.45: Exer. 150: Verify the identity.
 7.1.46: Exer. 150: Verify the identity.
 7.1.47: Exer. 150: Verify the identity.
 7.1.48: Exer. 150: Verify the identity.
 7.1.49: Exer. 150: Verify the identity.
 7.1.50: Exer. 150: Verify the identity.
 7.1.51: Exer. 5160: Show that the equation is not an identity. (Hint: Find ...
 7.1.52: Exer. 5160: Show that the equation is not an identity. (Hint: Find ...
 7.1.53: Exer. 5160: Show that the equation is not an identity. (Hint: Find ...
 7.1.54: Exer. 5160: Show that the equation is not an identity. (Hint: Find ...
 7.1.55: Exer. 5160: Show that the equation is not an identity. (Hint: Find ...
 7.1.56: Exer. 5160: Show that the equation is not an identity. (Hint: Find ...
 7.1.57: Exer. 5160: Show that the equation is not an identity. (Hint: Find ...
 7.1.58: Exer. 5160: Show that the equation is not an identity. (Hint: Find ...
 7.1.59: Exer. 5160: Show that the equation is not an identity. (Hint: Find ...
 7.1.60: Exer. 5160: Show that the equation is not an identity. (Hint: Find ...
 7.1.61: Exer. 6164: Either show that the equation is an identity or show th...
 7.1.62: Exer. 6164: Either show that the equation is an identity or show th...
 7.1.63: Exer. 6164: Either show that the equation is an identity or show th...
 7.1.64: Exer. 6164: Either show that the equation is an identity or show th...
 7.1.65: Exer. 6568: Refer to Example 5. Make the trigonometric substitution...
 7.1.66: Exer. 6568: Refer to Example 5. Make the trigonometric substitution...
 7.1.67: Exer. 6568: Refer to Example 5. Make the trigonometric substitution...
 7.1.68: Exer. 6568: Refer to Example 5. Make the trigonometric substitution...
 7.1.69: Exer. 6972: Make the trigonometric substitution x a tan for /2 < < ...
 7.1.70: Exer. 6972: Make the trigonometric substitution x a tan for /2 < < ...
 7.1.71: Exer. 6972: Make the trigonometric substitution x a tan for /2 < < ...
 7.1.72: Exer. 6972: Make the trigonometric substitution x a tan for /2 < < ...
 7.1.73: Exer. 7376: Make the trigonometric substitution x a sec for 0 < < /...
 7.1.74: Exer. 7376: Make the trigonometric substitution x a sec for 0 < < /...
 7.1.75: Exer. 7376: Make the trigonometric substitution x a sec for 0 < < /...
 7.1.76: Exer. 7376: Make the trigonometric substitution x a sec for 0 < < /...
Solutions for Chapter 7.1: Verifying Trigonometry Identities
Full solutions for Algebra and Trigonometry with Analytic Geometry  12th Edition
ISBN: 9780495559719
Solutions for Chapter 7.1: Verifying Trigonometry Identities
Get Full SolutionsAlgebra and Trigonometry with Analytic Geometry was written by and is associated to the ISBN: 9780495559719. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry with Analytic Geometry, edition: 12. Since 76 problems in chapter 7.1: Verifying Trigonometry Identities have been answered, more than 34744 students have viewed full stepbystep solutions from this chapter. Chapter 7.1: Verifying Trigonometry Identities includes 76 full stepbystep solutions.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

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.)

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

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

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.

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.

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

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

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 .

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

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

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.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

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).

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as 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!

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

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

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.