 4.3.4.3.1: Match the trigonometric function with its right triangle definition...
 4.3.4.3.2: Relative to the acute angle the three sides of a right triangle are...
 4.3.4.3.3: An angle that measures from the horizontal upward to an object is c...
 4.3.4.3.4: In Exercises 14, find the exact values of the six trigonometric fun...
 4.3.4.3.5: In Exercises 58, find the exact values of the six trigonometric fun...
 4.3.4.3.6: In Exercises 58, find the exact values of the six trigonometric fun...
 4.3.4.3.7: In Exercises 58, find the exact values of the six trigonometric fun...
 4.3.4.3.8: In Exercises 58, find the exact values of the six trigonometric fun...
 4.3.4.3.9: In Exercises 916, sketch a right triangle corresponding to the trig...
 4.3.4.3.10: In Exercises 916, sketch a right triangle corresponding to the trig...
 4.3.4.3.11: In Exercises 916, sketch a right triangle corresponding to the trig...
 4.3.4.3.12: In Exercises 916, sketch a right triangle corresponding to the trig...
 4.3.4.3.13: In Exercises 916, sketch a right triangle corresponding to the trig...
 4.3.4.3.14: In Exercises 916, sketch a right triangle corresponding to the trig...
 4.3.4.3.15: In Exercises 916, sketch a right triangle corresponding to the trig...
 4.3.4.3.16: In Exercises 916, sketch a right triangle corresponding to the trig...
 4.3.4.3.17: In Exercises 1726, construct an appropriate triangle to complete th...
 4.3.4.3.18: In Exercises 1726, construct an appropriate triangle to complete th...
 4.3.4.3.19: In Exercises 1726, construct an appropriate triangle to complete th...
 4.3.4.3.20: In Exercises 1726, construct an appropriate triangle to complete th...
 4.3.4.3.21: In Exercises 1726, construct an appropriate triangle to complete th...
 4.3.4.3.22: In Exercises 1726, construct an appropriate triangle to complete th...
 4.3.4.3.23: In Exercises 1726, construct an appropriate triangle to complete th...
 4.3.4.3.24: In Exercises 1726, construct an appropriate triangle to complete th...
 4.3.4.3.25: In Exercises 1726, construct an appropriate triangle to complete th...
 4.3.4.3.26: In Exercises 1726, construct an appropriate triangle to complete th...
 4.3.4.3.27: In Exercises 2742, complete the identity
 4.3.4.3.28: In Exercises 2742, complete the identity
 4.3.4.3.29: In Exercises 2742, complete the identity
 4.3.4.3.30: In Exercises 2742, complete the identity
 4.3.4.3.31: In Exercises 2742, complete the identity
 4.3.4.3.32: In Exercises 2742, complete the identity
 4.3.4.3.33: In Exercises 2742, complete the identity
 4.3.4.3.34: In Exercises 2742, complete the identity
 4.3.4.3.35: In Exercises 2742, complete the identity
 4.3.4.3.36: In Exercises 2742, complete the identity
 4.3.4.3.37: In Exercises 2742, complete the identity
 4.3.4.3.38: In Exercises 2742, complete the identity
 4.3.4.3.39: In Exercises 2742, complete the identity
 4.3.4.3.40: In Exercises 2742, complete the identity
 4.3.4.3.41: In Exercises 2742, complete the identity
 4.3.4.3.42: In Exercises 2742, complete the identity
 4.3.4.3.43: In Exercises 4348, use the given function value(s) and the trigonom...
 4.3.4.3.44: In Exercises 4348, use the given function value(s) and the trigonom...
 4.3.4.3.45: In Exercises 4348, use the given function value(s) and the trigonom...
 4.3.4.3.46: In Exercises 4348, use the given function value(s) and the trigonom...
 4.3.4.3.47: In Exercises 4348, use the given function value(s) and the trigonom...
 4.3.4.3.48: In Exercises 4348, use the given function value(s) and the trigonom...
 4.3.4.3.49: In Exercises 4956, use trigonometric identities to transform one si...
 4.3.4.3.50: In Exercises 4956, use trigonometric identities to transform one si...
 4.3.4.3.51: In Exercises 4956, use trigonometric identities to transform one si...
 4.3.4.3.52: In Exercises 4956, use trigonometric identities to transform one si...
 4.3.4.3.53: In Exercises 4956, use trigonometric identities to transform one si...
 4.3.4.3.54: In Exercises 4956, use trigonometric identities to transform one si...
 4.3.4.3.55: In Exercises 4956, use trigonometric identities to transform one si...
 4.3.4.3.56: In Exercises 4956, use trigonometric identities to transform one si...
 4.3.4.3.57: In Exercises 5762, use a calculator to evaluate each function. Roun...
 4.3.4.3.58: In Exercises 5762, use a calculator to evaluate each function. Roun...
 4.3.4.3.59: In Exercises 5762, use a calculator to evaluate each function. Roun...
 4.3.4.3.60: In Exercises 5762, use a calculator to evaluate each function. Roun...
 4.3.4.3.61: In Exercises 5762, use a calculator to evaluate each function. Roun...
 4.3.4.3.62: In Exercises 5762, use a calculator to evaluate each function. Roun...
 4.3.4.3.63: In Exercises 6368, find each value of in degrees and radians withou...
 4.3.4.3.64: In Exercises 6368, find each value of in degrees and radians withou...
 4.3.4.3.65: In Exercises 6368, find each value of in degrees and radians withou...
 4.3.4.3.66: In Exercises 6368, find each value of in degrees and radians withou...
 4.3.4.3.67: In Exercises 6368, find each value of in degrees and radians withou...
 4.3.4.3.68: In Exercises 6368, find each value of in degrees and radians withou...
 4.3.4.3.69: In Exercises 6976, find the exact values of the indicated variables...
 4.3.4.3.70: In Exercises 6976, find the exact values of the indicated variables...
 4.3.4.3.71: In Exercises 6976, find the exact values of the indicated variables...
 4.3.4.3.72: In Exercises 6976, find the exact values of the indicated variables...
 4.3.4.3.73: In Exercises 6976, find the exact values of the indicated variables...
 4.3.4.3.74: In Exercises 6976, find the exact values of the indicated variables...
 4.3.4.3.75: In Exercises 6976, find the exact values of the indicated variables...
 4.3.4.3.76: In Exercises 6976, find the exact values of the indicated variables...
 4.3.4.3.77: Height A sixfoot person walks from the base of a streetlight direc...
 4.3.4.3.78: Height A 30meter line is used to tether a heliumfilled balloon. B...
 4.3.4.3.79: Width A biologist wants to know the width w of a river (see figure)...
 4.3.4.3.80: Height of a Mountain In traveling across flat land you notice a mou...
 4.3.4.3.81: Angle of Elevation A zipline steel cable is being constructed for ...
 4.3.4.3.82: Inclined Plane The Johnstown Inclined Plane in Pennsylvania is one ...
 4.3.4.3.83: Machine Shop Calculations A steel plate has the form of one fourth ...
 4.3.4.3.84: Geometry Use a compass to sketch a quarter of a circle of radius 10...
 4.3.4.3.85: True or False? In Exercises 8587, determine whether the statement i...
 4.3.4.3.86: True or False? In Exercises 8587, determine whether the statement i...
 4.3.4.3.87: True or False? In Exercises 8587, determine whether the statement i...
 4.3.4.3.88: Think About It You are given the value Is it possible to find the v...
 4.3.4.3.89: Exploration (a) Use a graphing utility to complete the table. Round...
 4.3.4.3.90: Exploration Use a graphing utility to complete the table and make a...
 4.3.4.3.91: In Exercises 9194, use a graphing utility to graph the exponential ...
 4.3.4.3.92: In Exercises 9194, use a graphing utility to graph the exponential ...
 4.3.4.3.93: In Exercises 9194, use a graphing utility to graph the exponential ...
 4.3.4.3.94: In Exercises 9194, use a graphing utility to graph the exponential ...
 4.3.4.3.95: In Exercises 9598, use a graphing utility to graph the logarithmic ...
 4.3.4.3.96: In Exercises 9598, use a graphing utility to graph the logarithmic ...
 4.3.4.3.97: In Exercises 9598, use a graphing utility to graph the logarithmic ...
 4.3.4.3.98: In Exercises 9598, use a graphing utility to graph the logarithmic ...
Solutions for Chapter 4.3: Right Triangle Trigonometry
Full solutions for Precalculus With Limits A Graphing Approach  5th Edition
ISBN: 9780618851522
Solutions for Chapter 4.3: Right Triangle Trigonometry
Get Full SolutionsChapter 4.3: Right Triangle Trigonometry includes 98 full stepbystep solutions. Precalculus With Limits A Graphing Approach was written by and is associated to the ISBN: 9780618851522. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Precalculus With Limits A Graphing Approach, edition: 5. Since 98 problems in chapter 4.3: Right Triangle Trigonometry have been answered, more than 102894 students have viewed full stepbystep solutions from this chapter.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

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.

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.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

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

Diagonalization
A = S1 AS. A = eigenvalue matrix and S = eigenvector matrix of A. A must have n independent eigenvectors to make S invertible. All Ak = SA k SI.

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.

Hermitian matrix A H = AT = A.
Complex analog a j i = aU of a symmetric matrix.

Hessenberg matrix H.
Triangular matrix with one extra nonzero adjacent diagonal.

Iterative method.
A sequence of steps intended to approach the desired solution.

Orthonormal vectors q 1 , ... , q n·
Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q 1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.

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.

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

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

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

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.

Triangle inequality II u + v II < II u II + II v II.
For matrix norms II A + B II < II A II + II B II·

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.