 3.2.a: What is a radian?
 3.2.1: A radian is the measure of a central angle in a circle that cuts of...
 3.2.Problem 1: A central angle in a circle of radius 5 centimeters cuts off an arc...
 3.2.b: How is radian measure different from degree measure?
 3.2.2: When converting between degree measure and radian measure, use the ...
 3.2.Problem 2: Convert 50 to radians.
 3.2.c: Explain how to convert an angle from radians to degrees.
 3.2.3: Complete each statement regarding an angle and its reference angle ...
 3.2.Problem 3: Convert 430 to radians
 3.2.d: Explain how to convert an angle from degrees to radians.
 3.2.4: Match each angle (ad) with its corresponding radian measure (iiv)...
 3.2.Problem 4: Convert 47.5
 3.2.5: r 3 cm, s 9 cm 6.
 3.2.Problem 5: Convert to degrees.
 3.2.6: r 10 inches, s 5 inches
 3.2.Problem 6:
 3.2.7: r 12 inches, s 3inches 8.
 3.2.Problem 7: Convert to degrees.
 3.2.8: r 4 inches, s 12inches 9
 3.2.Problem 8: Find sin .
 3.2.9: r cm, s cm 1
 3.2.Problem 9:
 3.2.10: r cm, s cm
 3.2.Problem 10:
 3.2.11: Angle Between Cities Los Angeles and San Francisco are approximatel...
 3.2.Problem 11: Repeat Example 11, but use coordinates P1(N 36 43.403 , E 25 16.930...
 3.2.12: Angle Between Cities Los Angeles and New York City are approximatel...
 3.2.13: 30
 3.2.14: 135
 3.2.15: 260
 3.2.16: 340
 3.2.17: 150
 3.2.18: 120
 3.2.19: 420
 3.2.20: 390
 3.2.21: Use a calculator to convert 120 40 to radians. Round your answer to...
 3.2.22: Use a calculator to convert 256 20 to radians to the nearest hundre...
 3.2.23: Use a calculator to convert 1 (1 minute) to radians to three signif...
 3.2.24: Use a calculator to convert 1 to radians to three significant digits.
 3.2.25: Find the number of regular (statute) miles in 1 nautical mile to th...
 3.2.26: If two ships are 20 nautical miles apart on the ocean, how many sta...
 3.2.27: If two ships are 70 nautical miles apart on the ocean, what is the ...
 3.2.28: If the great circle distance between two ships on the ocean is 0.1 ...
 3.2.29: Clock Through how many radians does the minute hand of a clock turn...
 3.2.30: Clock Through how many radians does the minute hand of a clock turn...
 3.2.31: 3
 3.2.32: 6
 3.2.33: 2
 3.2.34: 2
 3.2.35: 2
 3.2.36: 3
 3.2.37: 2 5
 3.2.38: 2 3
 3.2.39: 2 3
 3.2.40: 4 3
 3.2.41: 7 6
 3.2.42: 3 4
 3.2.43: 7 4
 3.2.44: 11 6
 3.2.45: 3
 3.2.46: 4
 3.2.47: 4 3
 3.2.48: 11 6
 3.2.49: 7 6
 3.2.50: 5 3
 3.2.51: 11 4
 3.2.52: 7 3
 3.2.53: 1
 3.2.54: 2.4
 3.2.55: 0.25
 3.2.56: 5
 3.2.57: sin
 3.2.58: cos
 3.2.59: tan
 3.2.60: cot
 3.2.61: sec
 3.2.62: csc
 3.2.63: csc
 3.2.64: sec
 3.2.65: sin
 3.2.66: cos
 3.2.67: 4 cos
 3.2.68: 4 sin
 3.2.69: sin 2x
 3.2.70: cos 3x
 3.2.71: cos 2x
 3.2.72: 6 sin 3x
 3.2.73: 3 sin x
 3.2.74: 2 cos x
 3.2.75: sin x 76
 3.2.76: sin x 77
 3.2.77: 4 cos 2x 78
 3.2.78: 4 sin 3x 7
 3.2.79: 4 sin (3x ) 80
 3.2.80: 1 cos 2x Fo
 3.2.81: y sin x for x 0, , , , 82
 3.2.82: cos x for x 0, , , , 8
 3.2.83: y cos x for x 0, , , , 2 84.
 3.2.84: y sin x for x 0, , , , 2 85.
 3.2.85: y cos x for x 0, , , , 2 86
 3.2.86: y 2 sin x for x 0, , , , 2 87
 3.2.87: y sin 2x for x 0, , , , 8
 3.2.88: y cos 3x for x 0, ,
 3.2.89: cos x for
 3.2.90: y sin x for
 3.2.91: y 2 cos x for x 0, , , , 2 3
 3.2.92: y 3 sin x for x 0, , , , 2 93
 3.2.93: y 3 sin 2x for x , 0,
 3.2.94: y 5 cos 2x f
 3.2.95: Cycling The Campagnolo Hyperon carbon wheel has 22 spokes evenly di...
 3.2.96: Cycling The Reynolds Stratus DV carbon wheel has 16 spokes evenly d...
 3.2.97: P1(N 21 53.896 , W 159 36.336 ) Kauai, and P2(N 19 43.219 , W 155 0...
 3.2.98: P1(N 35 51.449 , E 14 28.668 ) Malta, and P2(N 36 24.155 , E 25 28....
 3.2.99: (1, 3)
 3.2.100: (1, 3)
 3.2.101: Find the remaining trigonometric functions of , if sin 1 2 and term...
 3.2.102: Find the remaining trigonometric functions of , if cos 2/2 and term...
 3.2.103: Find the six trigonometric functions of , if the terminal side of l...
 3.2.104: Find the six trigonometric functions of , if the terminal side of l...
 3.2.105: Find the radian measure of if is a central angle in a circle of rad...
 3.2.106: Convert 80 to radians. a. b. c. d
 3.2.107: Which of the following statements is false? a. cos 0 b. tan 3c. sin...
 3.2.108: Give the reference angle for . a. b. c. d.
Solutions for Chapter 3.2: Radians and Degrees
Full solutions for Trigonometry  7th Edition
ISBN: 9781111826857
Solutions for Chapter 3.2: Radians and Degrees
Get Full SolutionsSince 123 problems in chapter 3.2: Radians and Degrees have been answered, more than 26110 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Trigonometry, edition: 7. Chapter 3.2: Radians and Degrees includes 123 full stepbystep solutions. Trigonometry was written by and is associated to the ISBN: 9781111826857.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

CayleyHamilton Theorem.
peA) = det(A  AI) has peA) = zero matrix.

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

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

Full row rank r = m.
Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

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

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.

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.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

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

Orthogonal matrix Q.
Square matrix with orthonormal columns, so QT = Ql. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

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 •

Outer product uv T
= column times row = rank one matrix.

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

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Simplex method for linear programming.
The minimum cost vector x * is found by moving from comer to lower cost comer along the edges of the feasible set (where the constraints Ax = b and x > 0 are satisfied). Minimum cost at a comer!

Special solutions to As = O.
One free variable is Si = 1, other free variables = o.

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.