 3.1.1: An angle with its vertex at the center of a circle that intercepts ...
 3.1.2: 360 = radians, and 180 = radians.
 3.1.3: To convert to radians, multiply a degree measure by radian and simp...
 3.1.4: To convert to degrees, multiply a radian measure by and simplify
 3.1.5: CONCEPT PREVIEW Each angle u is an integer (e.g., 0, {1, {2,c) when...
 3.1.6: CONCEPT PREVIEW Each angle u is an integer (e.g., 0, {1, {2,c) when...
 3.1.7: CONCEPT PREVIEW Each angle u is an integer (e.g., 0, {1, {2,c) when...
 3.1.8: CONCEPT PREVIEW Each angle u is an integer (e.g., 0, {1, {2,c) when...
 3.1.9: CONCEPT PREVIEW Each angle u is an integer (e.g., 0, {1, {2,c) when...
 3.1.10: CONCEPT PREVIEW Each angle u is an integer (e.g., 0, {1, {2,c) when...
 3.1.11: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.12: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.13: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.14: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.15: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.16: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.17: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.18: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.19: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.20: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.21: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.22: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.23: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.24: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.25: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.26: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.27: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.28: Convert each degree measure to radians. Leave answers as multiples ...
 3.1.29: Convert each radian measure to degrees. See Examples 2(a) and 2(b) p 3
 3.1.30: Convert each radian measure to degrees. See Examples 2(a) and 2(b) ...
 3.1.31: Convert each radian measure to degrees. See Examples 2(a) and 2(b) ...
 3.1.32: Convert each radian measure to degrees. See Examples 2(a) and 2(b) ...
 3.1.33: Convert each radian measure to degrees. See Examples 2(a) and 2(b) ...
 3.1.34: Convert each radian measure to degrees. See Examples 2(a) and 2(b) ...
 3.1.35: Convert each radian measure to degrees. See Examples 2(a) and 2(b) ...
 3.1.36: Convert each radian measure to degrees. See Examples 2(a) and 2(b) ...
 3.1.37: Convert each radian measure to degrees. See Examples 2(a) and 2(b) ...
 3.1.38: Convert each radian measure to degrees. See Examples 2(a) and 2(b) ...
 3.1.39: Convert each radian measure to degrees. See Examples 2(a) and 2(b) ...
 3.1.40: Convert each radian measure to degrees. See Examples 2(a) and 2(b) ...
 3.1.41: Convert each radian measure to degrees. See Examples 2(a) and 2(b) ...
 3.1.42: Convert each radian measure to degrees. See Examples 2(a) and 2(b) ...
 3.1.43: Convert each radian measure to degrees. See Examples 2(a) and 2(b) 5p
 3.1.44: Convert each radian measure to degrees. See Examples 2(a) and 2(b) 15p
 3.1.45: Convert each degree measure to radians. If applicable, round to the...
 3.1.46: Convert each degree measure to radians. If applicable, round to the...
 3.1.47: Convert each degree measure to radians. If applicable, round to the...
 3.1.48: Convert each degree measure to radians. If applicable, round to the...
 3.1.49: Convert each degree measure to radians. If applicable, round to the...
 3.1.50: Convert each degree measure to radians. If applicable, round to the...
 3.1.51: Convert each degree measure to radians. If applicable, round to the...
 3.1.52: Convert each degree measure to radians. If applicable, round to the...
 3.1.53: Convert each degree measure to radians. If applicable, round to the...
 3.1.54: Convert each degree measure to radians. If applicable, round to the...
 3.1.55: Convert each degree measure to radians. If applicable, round to the...
 3.1.56: Convert each degree measure to radians. If applicable, round to the...
 3.1.57: Convert each radian measure to degrees. Write answers to the neares...
 3.1.58: Convert each radian measure to degrees. Write answers to the neares...
 3.1.59: Convert each radian measure to degrees. Write answers to the neares...
 3.1.60: Convert each radian measure to degrees. Write answers to the neares...
 3.1.61: Convert each radian measure to degrees. Write answers to the neares...
 3.1.62: Convert each radian measure to degrees. Write answers to the neares...
 3.1.63: Convert each radian measure to degrees. Write answers to the neares...
 3.1.64: Convert each radian measure to degrees. Write answers to the neares...
 3.1.65: Convert each radian measure to degrees. Write answers to the neares...
 3.1.66: Convert each radian measure to degrees. Write answers to the neares...
 3.1.67: Find each exact function value. See Example 3 sin p3
 3.1.68: Find each exact function value. See Example 3 cosp6
 3.1.69: Find each exact function value. See Example 3 tan p4
 3.1.70: Find each exact function value. See Example 3 cotp3
 3.1.71: Find each exact function value. See Example 3 sec p6
 3.1.72: Find each exact function value. See Example 3 csc p4
 3.1.73: Find each exact function value. See Example 3 sin p2
 3.1.74: Find each exact function value. See Example 3 csc p2
 3.1.75: Find each exact function value. See Example 3 tan 5p3
 3.1.76: Find each exact function value. See Example 3 cot2p3
 3.1.77: Find each exact function value. See Example 3 sin 5p6
 3.1.78: Find each exact function value. See Example 3 tan 5p6
 3.1.79: Find each exact function value. See Example 3 cos 3p
 3.1.80: Find each exact function value. See Example 3 sec p
 3.1.81: Find each exact function value. See Example 3 sin a  8p 3 b
 3.1.82: Find each exact function value. See Example 3 cot a  2p 3 b
 3.1.83: Find each exact function value. See Example 3 sin a  7p 6 b
 3.1.84: Find each exact function value. See Example 3 cos a  p 6 b
 3.1.85: Find each exact function value. See Example 3 tan a  14p 3 b
 3.1.86: Find each exact function value. See Example 3 csc a  13p 3 b
 3.1.87: Concept Check The figure shows the same angles measured in both deg...
 3.1.88: Concept Check What is the exact radian measure of an angle measurin...
 3.1.89: Concept Check Find two angles, one positive and one negative, that ...
 3.1.90: Concept Check Give an expression that generates all angles cotermin...
 3.1.91: Rotating Hour Hand on a Clock Through how many radians does the hou...
 3.1.92: Rotating Minute Hand on a Clock Through how many radians does the m...
 3.1.93: Orbits of a Space Vehicle A space vehicle is orbiting Earth in a ci...
 3.1.94: Rotating Pulley A circular pulley is rotating about its center. Thr...
 3.1.95: Revolutions of a Carousel A stationary horse on a carousel makes 12...
 3.1.96: Railroad Engineering Some engineers use the term grade to represent...
Solutions for Chapter 3.1: Radian Measure
Full solutions for Trigonometry  11th Edition
ISBN: 9780134217437
Solutions for Chapter 3.1: Radian Measure
Get Full SolutionsSince 96 problems in chapter 3.1: Radian Measure have been answered, more than 26033 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Trigonometry was written by and is associated to the ISBN: 9780134217437. This textbook survival guide was created for the textbook: Trigonometry, edition: 11. Chapter 3.1: Radian Measure includes 96 full stepbystep solutions.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Companion matrix.
Put CI, ... ,Cn in row n and put n  1 ones just above the main diagonal. Then det(A  AI) = ±(CI + c2A + C3A 2 + .•. + cnA nl  An).

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

GaussJordan method.
Invert A by row operations on [A I] to reach [I AI].

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , AjIb. Numerical methods approximate A I b by x j with residual b  Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.

Left nullspace N (AT).
Nullspace of AT = "left nullspace" of A because y T A = OT.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Particular solution x p.
Any solution to Ax = b; often x p has free variables = o.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

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.

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

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Symmetric factorizations A = LDLT and A = QAQT.
Signs in A = signs in D.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).