 Chapter 6.1: Find the radian measure that corresponds to each degree measure: 33...
 Chapter 6.2: Find the degree measure that corresponds to each radian measure:
 Chapter 6.3: A central angle is subtended by an arc 20 centimeters long on a cir...
 Chapter 6.4: (a) Find the length of the arc that subtends an angle of measure 70...
 Chapter 6.5: Two types of phonograph records, LP albums and singles, have diamet...
 Chapter 6.6: Using the information in Exercise 5, find the linear speed (in ) of...
 Chapter 6.7: Exer. 78: Find the exact values of x and y.
 Chapter 6.8: Exer. 78: Find the exact values of x and y.
 Chapter 6.9: Exer. 910: Use fundamental identities to write the first expression...
 Chapter 6.10: Exer. 910: Use fundamental identities to write the first expression...
 Chapter 6.11: Exer. 1120: Verify the identity by transforming the lefthand side i...
 Chapter 6.12: Exer. 1120: Verify the identity by transforming the lefthand side i...
 Chapter 6.13: Exer. 1120: Verify the identity by transforming the lefthand side i...
 Chapter 6.14: Exer. 1120: Verify the identity by transforming the lefthand side i...
 Chapter 6.15: Exer. 1120: Verify the identity by transforming the lefthand side i...
 Chapter 6.16: Exer. 1120: Verify the identity by transforming the lefthand side i...
 Chapter 6.17: Exer. 1120: Verify the identity by transforming the lefthand side i...
 Chapter 6.18: Exer. 1120: Verify the identity by transforming the lefthand side i...
 Chapter 6.19: Exer. 1120: Verify the identity by transforming the lefthand side i...
 Chapter 6.20: Exer. 1120: Verify the identity by transforming the lefthand side i...
 Chapter 6.21: If is an acute angle of a right triangle and if the adjacent side a...
 Chapter 6.22: Whenever possible, find the exact values of the trigonometric funct...
 Chapter 6.23: Find the quadrant containing if is in standard position
 Chapter 6.24: Find the exact values of the remaining trigonometric functions if
 Chapter 6.25: Exer. 2526: P(t) denotes the point on the unit circle U that corres...
 Chapter 6.26: Exer. 2526: P(t) denotes the point on the unit circle U that corres...
 Chapter 6.27: (a) Find the reference angle for each radian measure: ,,. (b) Find ...
 Chapter 6.28: Without the use of a calculator, find the exact values of the trigo...
 Chapter 6.29: Find the exact value. (a) (b)
 Chapter 6.30: If and is positive, approximate to the nearest 0.1
 Chapter 6.31: If , approximate to the nearest 0.0001 radian for .
 Chapter 6.32: If , approximate to the nearest 0.01 for
 Chapter 6.33: Exer. 3340: Find the amplitude and period and sketch the graph of t...
 Chapter 6.34: Exer. 3340: Find the amplitude and period and sketch the graph of t...
 Chapter 6.35: Exer. 3340: Find the amplitude and period and sketch the graph of t...
 Chapter 6.36: Exer. 3340: Find the amplitude and period and sketch the graph of t...
 Chapter 6.37: Exer. 3340: Find the amplitude and period and sketch the graph of t...
 Chapter 6.38: Exer. 3340: Find the amplitude and period and sketch the graph of t...
 Chapter 6.39: Exer. 3340: Find the amplitude and period and sketch the graph of t...
 Chapter 6.40: Exer. 3340: Find the amplitude and period and sketch the graph of t...
 Chapter 6.41: Exer. 4144: The graph of an equation is shown in the figure. (a) Fi...
 Chapter 6.42: Exer. 4144: The graph of an equation is shown in the figure. (a) Fi...
 Chapter 6.43: Exer. 4144: The graph of an equation is shown in the figure. (a) Fi...
 Chapter 6.44: Exer. 4144: The graph of an equation is shown in the figure. (a) Fi...
 Chapter 6.45: Exer. 4556: Sketch the graph of the equation.
 Chapter 6.46: Exer. 4556: Sketch the graph of the equation.
 Chapter 6.47: Exer. 4556: Sketch the graph of the equation.
 Chapter 6.48: Exer. 4556: Sketch the graph of the equation.
 Chapter 6.49: Exer. 4556: Sketch the graph of the equation.
 Chapter 6.50: Exer. 4556: Sketch the graph of the equation.
 Chapter 6.51: Exer. 4556: Sketch the graph of the equation.
 Chapter 6.52: Exer. 4556: Sketch the graph of the equation.
 Chapter 6.53: Exer. 4556: Sketch the graph of the equation.
 Chapter 6.54: Exer. 4556: Sketch the graph of the equation.
 Chapter 6.55: Exer. 4556: Sketch the graph of the equation.
 Chapter 6.56: Exer. 4556: Sketch the graph of the equation.
 Chapter 6.57: Exer. 5760: Given the indicated parts of triangle ABC with g 90 , a...
 Chapter 6.58: Exer. 5760: Given the indicated parts of triangle ABC with g 90 , a...
 Chapter 6.59: Exer. 5760: Given the indicated parts of triangle ABC with g 90 , a...
 Chapter 6.60: Exer. 5760: Given the indicated parts of triangle ABC with g 90 , a...
 Chapter 6.61: The length of the largest airplane propeller ever used was 22 feet ...
 Chapter 6.62: When the top of the Eiffel Tower is viewed at a distance of 200 fee...
 Chapter 6.63: Lasers are used to accurately measure velocities of objects. Laser ...
 Chapter 6.64: The Great Pyramid of Egypt is 147 meters high, with a square base o...
 Chapter 6.65: When viewed from Earth over a period of time, the planet Venus appe...
 Chapter 6.66: From a point 233 feet above level ground, a surveyor measures the a...
 Chapter 6.67: A ladder 16 feet long leans against the side of a building, and the...
 Chapter 6.68: A conical paper cup is constructed by removing a sector from a circ...
 Chapter 6.69: A tunnel for a new highway is to be cut through a mountain that is ...
 Chapter 6.70: When a certain skyscraper is viewed from the top of a building 50 f...
 Chapter 6.71: When a mountaintop is viewed from the point P shown in the figure, ...
 Chapter 6.72: An observer of height h stands on an incline at a distance d from t...
 Chapter 6.73: A spotlight with intensity 5000 candles is located 15 feet above a ...
 Chapter 6.74: n If a mountaintop is viewed from a point P due south of the mounta...
 Chapter 6.75: The manufacturer of a computerized projection system recommends tha...
 Chapter 6.76: A pyramid has a square base and congruent triangular faces. Let be ...
 Chapter 6.77: A surveyor, using a transit, sights the edge B of a bluff, as shown...
 Chapter 6.78: To simulate the response of a structure to an earthquake, an engine...
 Chapter 6.79: The variation in body temperature is an example of a circadian rhyt...
 Chapter 6.80: The annual variation in temperature T (in C) in Ottawa, Canada, may...
 Chapter 6.81: A reservoir supplies water to a community. During the summer months...
 Chapter 6.82: A cork bobs up and down in a lake. The distance from the bottom of ...
Solutions for Chapter Chapter 6: THE TRIGONOMETRIC FUNCTIONS
Full solutions for Algebra and Trigonometry with Analytic Geometry  12th Edition
ISBN: 9780495559719
Solutions for Chapter Chapter 6: THE TRIGONOMETRIC FUNCTIONS
Get Full SolutionsChapter Chapter 6: THE TRIGONOMETRIC FUNCTIONS includes 82 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry with Analytic Geometry, edition: 12. Algebra and Trigonometry with Analytic Geometry was written by and is associated to the ISBN: 9780495559719. Since 82 problems in chapter Chapter 6: THE TRIGONOMETRIC FUNCTIONS have been answered, more than 33602 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their 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.

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

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

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 II· Condition numbers measure the sensitivity of the output to change in the input.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

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

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.

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

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.

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.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and 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.

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).

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

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

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

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.

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