 1.1: Give the measures of the complement and the supplement of an angle ...
 1.2: Find the angle of least positive measure that is coterminal with ea...
 1.3: Find the angle of least positive measure that is coterminal with ea...
 1.4: Find the angle of least positive measure that is coterminal with ea...
 1.5: Work each problem. Rotating Propeller The propeller of a speedboat ...
 1.6: Work each problem. Rotating Pulley A pulley is rotating 320 times p...
 1.7: Convert decimal degrees to degrees, minutes, seconds, and convert d...
 1.8: Convert decimal degrees to degrees, minutes, seconds, and convert d...
 1.9: Convert decimal degrees to degrees, minutes, seconds, and convert d...
 1.10: Convert decimal degrees to degrees, minutes, seconds, and convert d...
 1.11: Find the measure of each marked angle.
 1.12: Find the measure of each marked angle.
 1.13: Find the measure of each marked angle.
 1.14: Find the measure of each marked angle.
 1.15: Length of a Road A camera is located on a satellite with its lens p...
 1.16: Express u in terms of a and b.
 1.17: Find all unknown angle measures in each pair of similar triangles.
 1.18: Find all unknown angle measures in each pair of similar triangles.
 1.19: Find the unknown side lengths in each pair of similar triangles.
 1.20: Find the unknown side lengths in each pair of similar triangles.
 1.21: In each figure, there are two similar triangles. Find the unknown m...
 1.22: In each figure, there are two similar triangles. Find the unknown m...
 1.23: Length of a Shadow If a tree 20 ft tall casts a shadow 8 ft long, h...
 1.24: Find the six trigonometric function values for each angle. Rational...
 1.25: Find the six trigonometric function values for each angle. Rational...
 1.26: Find the six trigonometric function values for each angle. Rational...
 1.27: Find the values of the six trigonometric functions for an angle in ...
 1.28: Find the values of the six trigonometric functions for an angle in ...
 1.29: Find the values of the six trigonometric functions for an angle in ...
 1.30: Find the values of the six trigonometric functions for an angle in ...
 1.31: Find the values of the six trigonometric functions for an angle in ...
 1.32: Find the values of the six trigonometric functions for an angle in ...
 1.33: An equation of the terminal side of an angle u in standard position...
 1.34: An equation of the terminal side of an angle u in standard position...
 1.35: An equation of the terminal side of an angle u in standard position...
 1.36: Complete the table with the appropriate function values of the give...
 1.37: Complete the table with the appropriate function values of the give...
 1.38: Concept Check If the terminal side of a quadrantal angle lies along...
 1.39: Give all six trigonometric function values for each angle u. Ration...
 1.40: Give all six trigonometric function values for each angle u. Ration...
 1.41: Give all six trigonometric function values for each angle u. Ration...
 1.42: Give all six trigonometric function values for each angle u. Ration...
 1.43: Give all six trigonometric function values for each angle u. Ration...
 1.44: Give all six trigonometric function values for each angle u. Ration...
 1.45: Decide whether each statement is possible or impossible. (a) sec u ...
 1.46: Concept Check If, for some particular angle u, sin u 6 0 and cos u ...
 1.47: Solve each problem Swimmer in Distress A lifeguard located 20 yd fr...
 1.48: Solve each problem Angle through Which the Celestial North Pole Mov...
 1.49: Solve each problem Depth of a Crater on the Moon The depths of unkn...
 1.50: Solve each problem Height of a Lunar Peak The lunar mountain peak H...
Solutions for Chapter 1: Trigonometric Functions
Full solutions for Trigonometry  11th Edition
ISBN: 9780134217437
Solutions for Chapter 1: Trigonometric Functions
Get Full SolutionsChapter 1: Trigonometric Functions includes 50 full stepbystep solutions. Trigonometry was written by and is associated to the ISBN: 9780134217437. Since 50 problems in chapter 1: Trigonometric Functions have been answered, more than 20315 students have viewed full stepbystep solutions from this chapter. This textbook survival guide was created for the textbook: Trigonometry, edition: 11. This expansive textbook survival guide covers the following chapters and their solutions.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

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

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.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Ellipse (or ellipsoid) x T Ax = 1.
A must be positive definite; the axes of the ellipse are eigenvectors of A, with lengths 1/.JI. (For IIx II = 1 the vectors y = Ax lie on the ellipse IIA1 yll2 = Y T(AAT)1 Y = 1 displayed by eigshow; axis lengths ad

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Length II x II.
Square root of x T x (Pythagoras in n dimensions).

Linearly dependent VI, ... , Vn.
A combination other than all Ci = 0 gives L Ci Vi = O.

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).

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

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.

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.

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

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.