 137.1: x = Cos1 _ 2 2
 137.2: Arctan 0 = x
 137.3: ARCHITECTURE The support for a roof is shaped like two right triang...
 137.4: Tan1 (_ 3 3 ) 5.
 137.5: Cos1 (1)
 137.6: cos (Cos1 _2 9)
 137.7: sin (Sin1 _3 4) 8
 137.8: sin (Cos1 _3 4) 9
 137.9: tan (Sin1 _1 2)
 137.10: x Cos1 _1 2 1
 137.11: Sin1 _1 2 x 1
 137.12: Arctan 1 x
 137.13: x Arctan _ 3 3 1
 137.14: x Sin1 ( _1 2 ) 15
 137.15: x Cos1 0
 137.16: Cos1 (_1 2) 17
 137.17: Sin1 _ 2 18
 137.18: Arctan _ 3 3
 137.19: Arccos _ 3 2 2
 137.20: sin (Sin1 _1 2) 2
 137.21: cot (Sin1 _5 6)
 137.22: tan (Cos1 _6 7) 2
 137.23: sin (Arctan _ 3 3 ) 24
 137.24: cos (Arcsin _3 5)
 137.25: TRAVEL The cruise ship Reno sailed due west 24 mi 48 mi Not drawn t...
 137.26: OPTICS You may have polarized sunglasses that eliminate glare by po...
 137.27: cot (Sin1 _7 9) 0.
 137.28: cos Tan1 3 0.5
 137.29: tan (Arctan 3)
 137.30: cos Arccos (_1 2)
 137.31: Sin1 (tan _ 4 ) 1.5
 137.32: cos (Cos1 _ 2 2 _ 2 ) 33.
 137.33: Cos1 (Sin1 90) 34
 137.34: sin (2 Cos1 _3 5) 0.
 137.35: sin (2 Sin1 _1 2) 0.8
 137.36: FOUNTAINS Architects who design fountains know that both the height...
 137.37: TRACK AND FIELD A shot put must land in a 40 sector. The vertex of ...
 137.38: Make a table of values, recording x and f(x) for x = {0, _1 2 , _ 2...
 137.39: Make a conjecture about f(x).
 137.40: Considering only positive values of x, provide an explanation of wh...
 137.41: OPEN ENDED Write an equation giving the value of the Cosine functio...
 137.42: Find the acute angle that the graph of 3x 5y 7 makes with the posit...
 137.43: Determine the obtuse angle formed at the intersection of the graphs...
 137.44: Explain why this relationship, tan m, holds true.
 137.45: Writing in Math Use the information on page 806 to explain how inve...
 137.46: ACT/SAT To the nearest degree, what is the angle of depression betw...
 137.47: REVIEW If sin = 23 and 90 90, then cos (2) = F  _1 9 . G  _1 3 ....
 137.48: sin 660 _
 137.49: cos 25
 137.50: (sin 135)2 (cos 675)2 1
 137.51: a 3.1, b 5.8, A 30
 137.52: a 9, b 40, c 41 c
 137.53: f(x) 5x2 6x 17 54.
 137.54: f(x) 3x2 2x 1 55.
 137.55: f(x) 4x2 10x 5 4
 137.56: PHYSICS A toy rocket is fired upward from the top of a 200foot tow...
Solutions for Chapter 137: Inverse Trigonometric Functions
Full solutions for Algebra 2, Student Edition (MERRILL ALGEBRA 2)  1st Edition
ISBN: 9780078738302
Solutions for Chapter 137: Inverse Trigonometric Functions
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Algebra 2, Student Edition (MERRILL ALGEBRA 2) was written by and is associated to the ISBN: 9780078738302. This textbook survival guide was created for the textbook: Algebra 2, Student Edition (MERRILL ALGEBRA 2), edition: 1. Since 56 problems in chapter 137: Inverse Trigonometric Functions have been answered, more than 45599 students have viewed full stepbystep solutions from this chapter. Chapter 137: Inverse Trigonometric Functions includes 56 full stepbystep solutions.

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

Column space C (A) =
space of all combinations of the columns of A.

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].

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.

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.

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

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

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

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

Orthogonal subspaces.
Every v in V is orthogonal to every w in W.

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

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

Row picture of Ax = b.
Each equation gives a plane in Rn; the planes intersect at x.

Schur complement S, D  C A } B.
Appears in block elimination on [~ g ].

Solvable system Ax = b.
The right side b is in the column space of A.

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

Subspace S of V.
Any vector space inside V, including V and Z = {zero vector only}.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.