 Chapter 13.1: When two angles in standard position have the same terminal side, t...
 Chapter 13.2: The Law of Sines is used to solve a triangle when the measure of tw...
 Chapter 13.3: Trigonometric functions can be defined by using a unit circle
 Chapter 13.4: For all values of , csc = _1 cos .
 Chapter 13.5: A radian is the measure of an angle on the unit circle where the ra...
 Chapter 13.6: In a coordinate plane, the initial side of an angle is the ray that...
 Chapter 13.7: Solve ABC by using the given measurements. Round measures of sides ...
 Chapter 13.8: Solve ABC by using the given measurements. Round measures of sides ...
 Chapter 13.9: Solve ABC by using the given measurements. Round measures of sides ...
 Chapter 13.10: Solve ABC by using the given measurements. Round measures of sides ...
 Chapter 13.11: Solve ABC by using the given measurements. Round measures of sides ...
 Chapter 13.12: Solve ABC by using the given measurements. Round measures of sides ...
 Chapter 13.13: A skateboarding ramp has an angle of elevation of 15.7. Its vertica...
 Chapter 13.14: Rewrite each degree measure in radians and each radian measure in d...
 Chapter 13.15: Rewrite each degree measure in radians and each radian measure in d...
 Chapter 13.16: Rewrite each degree measure in radians and each radian measure in d...
 Chapter 13.17: Rewrite each degree measure in radians and each radian measure in d...
 Chapter 13.18: Find one angle with positive measure and one angle with negative me...
 Chapter 13.19: Find one angle with positive measure and one angle with negative me...
 Chapter 13.20: Find one angle with positive measure and one angle with negative me...
 Chapter 13.21: Find one angle with positive measure and one angle with negative me...
 Chapter 13.22: Find one angle with positive measure and one angle with negative me...
 Chapter 13.23: Find the exact value of the six trigonometric functions of if the t...
 Chapter 13.24: Find the exact value of the six trigonometric functions of if the t...
 Chapter 13.25: Find the exact value of each trigonometric function.
 Chapter 13.26: Find the exact value of each trigonometric function.
 Chapter 13.27: The formula R = V0 2 _ sin 2 32 gives the distance of a baseball th...
 Chapter 13.28: Determine whether each triangle has no solution, one solution, or t...
 Chapter 13.29: Determine whether each triangle has no solution, one solution, or t...
 Chapter 13.30: Determine whether each triangle has no solution, one solution, or t...
 Chapter 13.31: Determine whether each triangle has no solution, one solution, or t...
 Chapter 13.32: Determine whether each triangle has no solution, one solution, or t...
 Chapter 13.33: Two fishing boats, A, and B, are anchored 4500 feet apart in open w...
 Chapter 13.34: Determine whether each triangle should be solved by beginning with ...
 Chapter 13.35: Determine whether each triangle should be solved by beginning with ...
 Chapter 13.36: Determine whether each triangle should be solved by beginning with ...
 Chapter 13.37: Determine whether each triangle should be solved by beginning with ...
 Chapter 13.38: Determine whether each triangle should be solved by beginning with ...
 Chapter 13.39: Determine whether each triangle should be solved by beginning with ...
 Chapter 13.40: Find the exact value of each function.
 Chapter 13.41: Find the exact value of each function.
 Chapter 13.42: Find the exact value of each function.
 Chapter 13.43: Find the exact value of each function.
 Chapter 13.44: Find the exact value of each function.
 Chapter 13.45: Find the exact value of each function.
 Chapter 13.46: A Ferris wheel with a diameter of 100 feet completes 2.5 revolution...
 Chapter 13.47: Find each value. Write angle measures in radians. Round to the near...
 Chapter 13.48: Find each value. Write angle measures in radians. Round to the near...
 Chapter 13.49: Find each value. Write angle measures in radians. Round to the near...
 Chapter 13.50: Find each value. Write angle measures in radians. Round to the near...
 Chapter 13.51: The equation y = Arctan 1 describes the counterclockwise angle thro...
Solutions for Chapter Chapter 13: Trigonometric Functions
Full solutions for California Algebra 2: Concepts, Skills, and Problem Solving  1st Edition
ISBN: 9780078778568
Solutions for Chapter Chapter 13: Trigonometric Functions
Get Full SolutionsCalifornia Algebra 2: Concepts, Skills, and Problem Solving was written by and is associated to the ISBN: 9780078778568. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: California Algebra 2: Concepts, Skills, and Problem Solving, edition: 1. Chapter Chapter 13: Trigonometric Functions includes 51 full stepbystep solutions. Since 51 problems in chapter Chapter 13: Trigonometric Functions have been answered, more than 44153 students have viewed full stepbystep solutions from this chapter.

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.

Block matrix.
A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

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

Column picture of Ax = b.
The vector b becomes a combination of the columns of A. The system is solvable only when b is in the column space C (A).

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

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].

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

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.

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.

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].

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.

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

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.

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

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!

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

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

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

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.