 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 35839 students have viewed full stepbystep solutions from this chapter.

Adjacency matrix of a graph.
Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected). Adjacency matrix of a graph. Square matrix with aij = 1 when there is an edge from node i to node j; otherwise aij = O. A = AT when edges go both ways (undirected).

Affine transformation
Tv = Av + Vo = linear transformation plus shift.

Associative Law (AB)C = A(BC).
Parentheses can be removed to leave ABC.

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).

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

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

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].

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

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.

Hypercube matrix pl.
Row n + 1 counts corners, edges, faces, ... of a cube in Rn.

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

Lucas numbers
Ln = 2,J, 3, 4, ... satisfy Ln = L n l +Ln 2 = A1 +A~, with AI, A2 = (1 ± /5)/2 from the Fibonacci matrix U~]' Compare Lo = 2 with Fo = O.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

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

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.

Rotation matrix
R = [~ CS ] rotates the plane by () and R 1 = RT rotates back by (). Eigenvalues are eiO and eiO , eigenvectors are (1, ±i). c, s = cos (), sin ().

Standard basis for Rn.
Columns of n by n identity matrix (written i ,j ,k in R3).

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