conversations.from: human
conversations.value: What could be a title for a book about with the genre: Science & Math, Mathematics?
conversations.from: assistant
conversations.value: A title for this book could be 'Pre-Calculus Workbook For Dummies'
conversations.from: human
conversations.value: What is the first four paragraphs for this book?
conversations.from: assistant
conversations.value: Pre-Calculus Workbook For Dummies
  And last, but not least, I am forever grateful to my wife, Aijun, for her beautiful creation of and the great attention she devotes to the family, so that I can have time to do my work, including carrying out this project.
  Throughout my varied career I have had the great pleasure of working with professionals of many disciplines. The For Dummies series combines the skills of many very talented people. I want to express my gratitude to Bill Gladstone who gave me this rare opportunity to participate; to the editors at Wiley — Lindsay Lefevere, Tracy Boggier, Elizabeth Rea, and Christy Pingleton — for their professionalism, understanding, and skill in bringing such a complex product to market; and to Yang Kuang who juggled his demanding teaching schedule to accommodate this project.
  First we review basic material from Algebra II. We then cover real numbers and what you'll be asked to do with them. Next up are functions of all kinds (polynomials, rational, exponential, and logarithmic): graphing them and performing operations with them.
  The chapters in Part II review trig ratios and word problems for trig. We show you how to build the unit circle, how to solve trig equations, and how to graph trig functions. Some of these topics may be review for you as well; that really depends on how much trig was covered in your Algebra II course.
conversations.from: human
conversations.value: What is five more paragraphs?
conversations.from: assistant
conversations.value: Begin by using co-function identities to replace each term. Then use ratio identities to replace the sine/cosine fraction with tangent. Finally, multiply the tangent terms.
  Start by replacing terms using co-function identities. Next, use reciprocal and ratio identities to rewrite the terms using sine and cosine. Then, because the first two terms have a common denominator of sine, you can write them as a single fraction. Next, you can multiply using FOIL. The resulting numerator can be simplified using a Pythagorean identity. Finally, cancel sine from the numerator and denominator.
  Using periodicity identities, replace each term. Then, using ratio identities, replace the cotangent with a ratio of cosine and sine.
  Ah! Don't let this one trick you. 4π is a multiple of 2π, so adding that to x also gives you a periodicity identity. Replacing the terms with the appropriate periodicity identity, you can easily simplify this problem. The next step is to use ratio identities to replace the cotangent term with a ratio of cosine and sine. Then, simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator. Cancel where you can to get a simplified expression.
  Start by replacing both terms using periodicity identities. Then, you can rewrite the fraction as a division problem. Next, rewrite the division problem by multiplying by the reciprocal. Then use reciprocal identities to replace both terms. Multiply to write as a single term, which can be simplified using ratio identities.
conversations.from: human
conversations.value: Add another sentence about Cancel.
conversations.from: assistant
conversations.value: Begin by using co-function identities to replace each term. Then use ratio identities to replace the sine/cosine fraction with tangent. Finally, multiply the tangent terms. 
  Start by replacing terms using co-function identities. Next, use reciprocal and ratio identities to rewrite the terms using sine and cosine. Then, because the first two terms have a common denominator of sine, you can write them as a single fraction. Next, you can multiply using FOIL. The resulting numerator can be simplified using a Pythagorean identity. Finally, cancel sine from the numerator and denominator. 
  Using periodicity identities, replace each term. Then, using ratio identities, replace the cotangent with a ratio of cosine and sine. Cancel the sine from the numerator and denominator and add the two cosines. 
  Ah! Don't let this one trick you. 4π is a multiple of 2π, so adding that to x also gives you a periodicity identity. Replacing the terms with the appropriate periodicity identity, you can easily simplify this problem. The next step is to use ratio identities to replace the cotangent term with a ratio of cosine and sine. Then, simplify the complex fraction by multiplying the numerator by the reciprocal of the denominator. Cancel where you can to get a simplified expression. 
  Start by replacing both terms using periodicity identities. Then, you can rewrite the fraction as a division problem. Next, rewrite the division problem by multiplying by the reciprocal. Then use reciprocal identities to replace both terms. Multiply to write as a single term, which can be simplified using ratio identities.
conversations.from: human
conversations.value: What is the last five paragraphs?
conversations.from: assistant
conversations.value: When it comes to roots, we've seen all kinds of errors. For instance,  suddenly becomes 3 in a problem and loses the root altogether.
  When multiplying monomials, don't multiply the exponents. We've seen students who've been dealing with exponents for a long time suddenly do something like this:
  You can cancel terms when adding or subtracting if you have two terms that are exact opposites of each other. In multiplication and division, you can cancel terms if one common factor divides into all terms.
  When a polynomial is multiplied by a monomial, the process is known as distribution. Think of it like delivering the newspaper to every house on the block.
  We've also seen students who don't distribute to every term, especially when the polynomial gets long.
conversations.from: human
conversations.value: Reverse the sentences.
conversations.from: assistant
conversations.value: We've also seen students who don't distribute to every term, especially when the polynomial gets long.. Think of it like delivering the newspaper to every house on the block.
  When a polynomial is multiplied by a monomial, the process is known as distribution. In multiplication and division, you can cancel terms if one common factor divides into all terms. We've seen students who've been dealing with exponents for a long time suddenly do something like this:
  You can cancel terms when adding or subtracting if you have two terms that are exact opposites of each other.
  When multiplying monomials, don't multiply the exponents. For instance,  suddenly becomes 3 in a problem and loses the root altogether.When it comes to roots, we've seen all kinds of errors