Precalculus links & errata

Below are some of the links that are referenced in the book Precalculus. (Note: Art of Problem Solving is not responsible for the content on any external site.)

How to Use This Book

Mandelbrot links

Transformations of the Complex plane

Unfortunately, the book is not perfect. If you find an error in the text or solutions, we would appreciate a short email to books@artofproblemsolving.com describing the error.

First printing errata

Text:

• Page xiv. The equation in the third line should read f(0) = 0^2 + 2i = 2i.
• Chapter 2, page 42. The angle in the equilateral triangle should be pi/3.
• Chapter 2, pages 64-66, Problem 2.28. Problem 2.28 and its solution should be replaced with this correction. Both the problem and the solution have changes from the text.
• Chapter 3, page 89, Problem 3.5. The solution given for part (e) is the solution to part (d). (There is no part (e)!)
• Chapter 3, page 125, Problem 3.35. The equations sin(-x) = sin x and cos(-x) = -cos x are incorrect, and should be sin(-x) = -sin x and cos(-x) = cos x.
• Chapter 8, page 274. The final equation in the solution to Problem 8.17 should be replaced with "lines AB and CD are perpendicular".
• Chapter 8, page 293. In the first centered equation atop the page, the 1/(abcd) on the far right side should be 1/(abcz), and similarly for the ensuing string of equations.
• Chapter 10, page 338. In the final paragraph of text, the equation f(v+w) = f(v+w) should be f(v+w) = f(v) + f(w).
• Chapter 11, page 382, Problem 11.1(c). The equation 2x+1=0 should be 2x-1=0, and the equation x=-1/2 should be x=1/2.
• Chapter 12, page 423, Problem 12.2. The triplet representing the points on line CD should have -2+3u as the second component, not 2+3u. This error is propagated through the remainder of the solution, though it does not change the final conclusion that the lines do not intersect.
• Chapter 12, page 426, Problem 12.4(a). There should not be a coefficient of t on the final vector in the second line of the solution.
• Chapter 12, page 442, Problem 12.2.5. The equation should be 2x - y + 3z = 5.

Solutions:

• Chapter 2, page 20, Problem 2.4.6. The answer should be 1.68 meters, not 1.68 feet.
• Chapter 3, Problem 3.52, page 49. The solution set should include 0.
• Chapter 5, Problem 5.3.1(b), page 90. The answer should be (6, 0, 5*pi/6).
• Chapter 5, Problem 5.3.5(b), page 91. The boxed answer should be (r, theta + pi, z).
• Chapter 5, Problem 5.29(a), page 94. The angle should be 5pi/4, not 7pi/4, which is approximately 3.93 radians.
• Chapter 12, Problem 12.41(a), page 229. The last line of the first paragraph should read, "which means u - v = 0, or u = v."

Second printing errata (see the bottom of the title page to determine if you have a book from the second printing)

Text:

• Chapter 2, pages 64-66, Problem 2.28. Problem 2.28 and its solution should be replaced with this correction. Both the problem and the solution have changes from the text.
• Chapter 7, page 249, Problem 7.4.2. The complex number w should be a primitive 13th root of unity.
• Chapter 11, page 404. Equations (11.5) and (11.6) have the wrong final 2x2 determinant in each. So the top line of (11.5) should read:
  
  and the top line of (11.6) should read:
  
• Chapter 12, page 423, Problem 12.2. The triplet representing the points on line CD should have -2+3u as the second component, not 2+3u. This error is propagated through the remainder of the solution, though it does not change the final conclusion that the lines do not intersect.
• Chapter 12, page 442, Problem 12.2.5. The equation should be 2x - y + 3z = 5.

Solutions:

• Chapter 2, page 20, Problem 2.4.6. The answer should be 1.68 meters, not 1.68 feet.
• Chapter 5, Problem 5.3.1(b), page 90. The answer should be (6, 0, 5*pi/6).
• Chapter 5, Problem 5.29(a), page 94. The angle should be 5pi/4, not 7pi/4, which is approximately 3.93 radians.