What is Precalculus: Definition and 174 Discussions

In mathematics education, precalculus or college algebra is a course, or a set of courses, that includes algebra and trigonometry at a level which is designed to prepare students for the study of calculus. Schools often distinguish between algebra and trigonometry as two separate parts of the coursework.

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  1. Y

    MHB Precalculus help --> cos2x=3/5 and 90<x<180

    Hello, can someone please help me with this problem? I have to find the values of the 6 trig functions if the conditions provided hold cos2(theta)=3/5 90 degrees is less than or equal to theta, and theta is also less than or equal to 180 degrees THANK you so much.
  2. Sandro Romualdez

    Vectors: Proving the value of a•(b x c)

    Homework Statement Given that vector a = (1, 2, -5), b = (-12, 41, 75) and c = a + 2b, explain why (without doing any calculations whatsoever) the value of a•(b x c) = 0 Homework Equations No specific equations, as the question asks for the value without making any calculations. This problem...
  3. M

    MHB Can You Name 9 Important Precalculus Topics for a Strong Foundation in Calculus?

    If you were to make a list of 10 important precalculus topics that students should know very well, what would they be? Let me start by saying word problems. All students going into Calculus 1 should be able to answer Algebra 1 and 2 applications. Can you name 9 other important precalculus...
  4. M

    MHB Is Precalculus Worth Learning in 2018?

    I will return in January 2018 with more precalculus questions. I will try to learn LaTex. I need this site to help me increase my math skills. I am ok with basics but I want to advance my knowledge of mathematics. I may never use it in real life but math is fun and interesting.
  5. N

    B Why do equations with two distinct variables with 2 distinct

    My question is about basic algebra. I am thinking about the "why" here and I'm looking for an intuitive answer.If you have the following equations: =>S+U=90 =>S+U=90 and =>40S+25U=2625 =>40S+25U=2625 you can then rewrite S=90−U and then substitute. Now you have a single equation with one...
  6. M

    Transforming Piecewise Functions

    Homework Statement The piece wise function is -x-2, x<-1 x^2-3x, -1≤ x ≤5 3x+5, x>5 The problem is to transform the function with...
  7. M

    MHB Is Precalculus Necessary for Success in Calculus 1?

    Algebra 2, intermediate algebra and college algebra cover most of the topics taught in precalculus. Taking geometry and then trigonometry prepares anyone for calculus 1. So, is precalculus really needed as a prerequisite for calculus 1?
  8. S

    Calculus Need help preparing for Courant's Calculus

    Hello, Just to give you some background info, I'm a software developer looking to make a career switch to Mechanical Engineering (At least I think so). My interests lie in design, complex systems, maglev, rockets and new forms of space propulsion. Before I really commit myself to University, I...
  9. M

    MHB Precalculus Chapter Test Questions

    I would like to share chapter test questions from the David Cohen Precalculus With Unit Circle Trigonometry textbook (3rd Edition) as extra practice for anyone who may be interested. Where in this website can I post precalculus chapter test questions?
  10. M

    MHB Is MathTV the Number One Online Resource for Precalculus Help?

    From now on, I will not post questions from each chapter of the precalculus textbook. I realize now that this site is not for that purpose. I will only post questions from the textbook that are interestingly hard.
  11. Grey_Thunderhead

    Find ground speed and direction of airplane

    Homework Statement [/B] "An airplane is flying on a bearing of 340 degrees at 400mph. A wind is blowing at a bearing of 320 degrees at 30mph. Find ground speed and direction of the plane." Homework Equations vx=vcosϕ vy=vsinϕ The Attempt at a Solution [/B] First, my teacher told us to change...
  12. M

    MHB Most Important Precalculus Topics

    In your opinion, what are the most important topics in precalculus needed before entering calculus 1? What must a student know well after taking precalculus?
  13. M

    MHB Why is Precalculus such a challenging course for students?

    Algebra 2, Trigonometry, Intermediate Algebra and College Algebra cover most topics presented in a Precalculus course. My first question is simple: What is the purpose for a Precalculus course?
  14. Schaus

    Logarithm question using compound interest formula

    Homework Statement A colony of ants will grow by 12% per month. If the colony originally contains 2000 ants how long will it take for the colony to double in size? Answer - 6.12 months Homework Equations A = P(1+r/n)nt The Attempt at a Solution r = 12% = 0.12 n = 12 P = 2000 A = 4000 t = ...
  15. Schaus

    Graphing Rational Functions: How to Find Asymptotes and Intercepts

    Homework Statement Sketch the graphs of the following functions and show all asymptotes with a dotted line y = (2x - 6)/ (x2-5x+4) i) Equation of any vertical asymptote(s) ii) State any restrictions or non-permissible value(s) iii) Determine coordinates of any intercept(s) iv) Describe the...
  16. O

    Schools Answering Questions about Precalculus & Trig

    Is this precalculus minus trig?
  17. franktherabbit

    Find the limit of the expression

    Homework Statement $$\lim_{x\to\infty} \left(\frac{n^2+2n+1}{n^2+2n+3}\right)^{\frac{2n^2}{n+1}}$$ Homework Equations 3. The Attempt at a Solution [/B] I tried ##\lim_{x\to\infty} \left(\frac{n^2+2n+3-2}{n^2+2n+3}\right)^{\frac{2n^2}{n+1}}=## ##\lim_{x\to\infty}...
  18. F

    Foundations I have complied a list of textbooks about Trig, Algebra, Etc

    I am planning to self-teach myself Trigonometry and all the other required fields before jumping into calculus. I have compiled a list of books that I have researched and would like your opinions and recommendations. Books: Precalculus Mathematics in a Nutshell: Geometry, Algebra, Trigonometry...
  19. J

    Can't find all the zeroes of a polynomial

    Homework Statement Help i have a homework quiz done and i simply can't find out how to do the 3rd problem as we haven't even learned how to do it or maybe my notes aren't good or something , however I am close to an A in the class and this would help bring it closer. It asks me: "Find all the...
  20. A

    Calculus Calculus 1 text book - Need review of precalculus

    Hi, so I'm taking calculus 1 this year however I haven't taken precalculus in several years. I don't remember any of it, and the textbook of the course doesn't review it at all(they just sample you questions) and I'm having issues solving the precalculus review questions(how necessary is it that...
  21. L

    What Are the Values of c and d for This Precalculus Limit Problem?

    Homework Statement limit as x approaches 2 of [ (x^2-cx+d)/(x^2-4) ] = 3. What is the value of c and d? Homework Equations Limits The Attempt at a Solution I tried cross multiplying to get (x^2 - cx + d) = 3x^2 - 12, and I was thinking of moving combining like terms and maybe factoring but I...
  22. N

    I can't understand this problem

    Homework Statement Ok so this isn't really a problem, more like a problem set, I'm not sure if I'm able to understand it yet. The context is determining all the primitive pythogrean triples Letting x = a/c and y = b/c, we see that (x, y) is a point on the unit circle with rational number...
  23. U

    What do I need to master before I start calculus?

    I want to start learning calculus I. But, I don't know what courses I need to finish before starting precalculus. any help would be appreciated.
  24. W

    How Do I Calculate the Angle Between Vectors in Vector Projection Problems?

    Homework Statement http://imgur.com/a/Yq8pWHomework Equations projection u onto v: ((u x v)/(||v||^2)) x v Unit vector: u/||u|| The Attempt at a Solution For number 2, I absolutely do not know how to set up the problem. I do not know what vectors to use, I assumed F vector to be <0.00375...
  25. V

    What is the common root for two polynomial equations with a shared coefficient?

    Homework Statement [/B] Th value of 'a' for which the equation x3+ax+1=0 and x4+ax+1=0 have a common root is?Homework EquationsThe Attempt at a Solution i initially thought of subtracting both the equations and then finding x and substituting back in the equation but it did not work.
  26. V

    A permutation and combination problem

    .The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices (0, 0), (0, 41) and (41, 0), is (1) 901 (2) 861 (3) 820 (4) 780 my attempt: for this to be true i know that sum of x and y coordinate should be 41 but i don't know how to proceed.
  27. C

    Trig Identities: Simplifying Expressions with Cotangent, Secant, and Cosecant

    I have re-post this forum as I should have paid closer attention to rules. I apologized for that. Homework Statement 1) The expression tan^3 θ + sinθ/cosθ is equal to: (a) cot θ (b) tan θ sec^2 θ (c) tan θ (d) sin θ tan θ (e) tan θ csc^2 θ 2) Simplify (cos θ/1+ sin θ - cosθ/sinθ-1)^-1 (a)...
  28. HRubss

    Stuck on a question from Precalculus 2

    Homework Statement "A small radio transmitter broadcasts in a 25 mile radius. If you drive along a straight line from a city 30 miles north of the transmitter to a second city 33 miles east of the transmitter, during how much of the drive will you pick up a signal from the transmitter?"Homework...
  29. D

    Find the sets of real solutions

    [b[1. Homework Statement [/b] ##|4^{3x}-2^{4x+2}*3^{x+1}+20*12^x*3^x| \ge 8*6^x(8^{x-1}+6^x)## The sets containing the real solutions for some numbers ##a, b, c, d,## such that ##-\infty < a < b < c < d < +\infty## is of the form ##(-\infty, a] \cup [b, c] \cup [d, +\infty)##. Prove it by...
  30. D

    Find real solutions to an equation

    Homework Statement log(cosx)sinx = 4*log(sinx)cosx Homework Equations 3. The Attempt at a Solution i tried to solve it and uploaded my work but my last part reads (cosx)^2 = sinx (cosx)^(-2) = sinx its weird that i don't see where i have made a mistake[/B]
  31. D

    Area of a triangle under a curve

    Homework Statement The tangent line of a curve y=e^(-x) intercepts the axises at points A and B. What is the maximum area of a triangle AOB considering O as the origin. Homework Equations Ar= xy/2 The Attempt at a Solution Derivative of this function is y'=-e^(-x) I took the formula of the...
  32. D

    Trigonometric Problem: Solving for sin(x/2)*cos(5p/4) with Given Conditions

    Homework Statement cos(x - 3p/2) = - 4/5 p <x< p/2 sin(x/2)*cos(5p/4)= ? Homework Equations The Attempt at a Solution I made it as far as to determine that sinx= 4/5 and cosx = - 3/5 but can't seems to progress any further. I am looking for an easier way to find the solution without having to...
  33. D

    Can Logarithmic Properties Simplify This Equation?

    Homework Statement For clarification a have posted the equation below as a picture file.[/B] Homework Equations log(a*b)= loga + logb log(a/b) = loga-logb log(a^n) = nloga[/B] The Attempt at a Solution I don't know how to start. I can't remember the rule for powering the logarithms if there...
  34. D

    Finding the quadratic equation that suits the solutions

    Homework Statement if x1 and x2 are solutions to 1) x² + x + 1 = 0, then 2) y1 = ax1 + x2 and 3) y2 = x1 + ax2 are solutions to which quadratic equation? Homework Equations ax² + bx + c = 0 x1∕2 = (−b ± √(b² - 4ac))/2a The Attempt at a Solution Well, firstly i solved for x1 and x2 getting...
  35. D

    Calculus Best math textbook covering these topics?

    Hi everyone! I am starting to prepare for my admission test into college next year and I am looking for a best textbook which covers these topics ( with an adition of other it may also include but not disclude these) Polynomials Functions ( linear, quadratic ) Algebraic equations and...
  36. F

    Combinatorics question: Identical/nonidentical

    Homework Statement and attempt at a solution[/B] If 5 gifts are to be given among 8 children: a) if the gifts are identical (indistinguishable) and no child can receive more than 1 gift, there are 8P5 ways b) if the gifts are non-identical (distinguishable) there are 5!(8P5) ways In a), the...
  37. S

    Calculus Good precalculus and calculus book for a beginner for physic

    Hi I'm 16 years old, the physics and maths in school is really easy and it quickly becomes boring. So I wish to study outside of school, can you please recommend me some good books on calculus? I am a beginner in the subject and only know the big picture of what calculus actually is, so...
  38. B

    R^2=9cos(3Ө) Convert to rectangular cordinates

    Homework Statement Homework EquationsThe Attempt at a Solution -In order for me to figure out this problem I had to reverse the equality to isolate the Ө on the left side making the new equation 9cos(3Ө)=r^2. The first thing I’m going to do is change cos(3Ө) in terms of cos and sin. That will...
  39. K

    Foundations Theoretical Books on Mathematics

    What are some rigorous theoretical books on mathematics for each branch of it? I have devised a fantastic list of my own and would like to hear your sentiments too. Elementary Algebra: Gelfand's Algebra Gelfand's Functions & Graphs Burnside's Theory of Equations Euler's Analysis of the...
  40. Alfie Simpson

    How do I teach myself precalculus up to calculus?

    What are some good textbooks, websites, question papers and other sources of information that will help me teach myself precalculus up to calculus? How long will this take until I have a good grasp of the knowledge?
  41. Curieuse

    Rational and irrational numbers

    Homework Statement Determine a positive rational number whose square differs from 7 by less than 0.000001 (10^(-6)) Homework Equations - The Attempt at a Solution Let p/q be the required rational number. So, 7> (p/q)^(2) > 7-(0.000001) ⇒ √(7) > p/q > √(7-.000001) ⇒√(7) q> p >...
  42. B

    Foundations Seeking Your Advice on Pre-Calculus Books Selection

    Dear Physics Forum personnel, I wrote this email because I am seeking a recommendation on selecting the pre-calculus textbooks. I have been studying the real analysis and number theory, and I felt that I need to brush up the algebra, functions, trigonometry, and geometry. So I decided to...
  43. Adriane

    I'm having trouble creating my own trig function

    I'm developing my own trigonometric function concerning a "real world" problem of my choosing. I decided to go with the orbit of Neptune around the sun. I just don't know how to develop the equation itself, like if it would be sine or cosine? I'm just lost as to where to begin. If anyone can...
  44. Ravenalia

    How Can I Get Help with Physics on the Physics Forums?

    Hiya, my name's Raven, and I have a lot of problems with physics. I often have trouble with (you guessed it) MASTERING PHYSICS! I used this site a number of times for homework help prior to joining (primarily because most other sites for physics help are blocked on my school computer), so I...
  45. N

    Precalculus -- determine the rate of change of the function

    Homework Statement Homework Equations Rate of change formula: y2-y1/x2-y2 The Attempt at a Solution If this is a rate of change problem so I use the rate of change formula: y2-y1/x2-y2 and since it's from 2 to 4 I think that would be (2,0) (4,0) and thus (0-0)/(4-2) = 0/2 = 0 I don't...
  46. Eclair_de_XII

    How are precalculus and analytical geometry different?

    I'm really stressed out at where I should be in my college career. In high school, I had taken trigonometry and analytical geometry. But when I went to college and took calculus, I was completely dumbfounded on what was being taught. I felt like I should have known the material. Google tells me...
  47. P

    Rigorous Precalculus and Calculus Textbooks + Intro to Linear Algebra

    I am currently studying A level Further Pure Mathematics, and I will be joining university next year. I want to brush up on precalculus (algebra, trigonometry, geometry) and calculus (differential, integral [single variable]), except that this time I need a more rigorous treatment of those...
  48. M

    Proof by Induction: Sum of 2^n - 1 Explained Step by Step

    Homework Statement 1 + 2 + 2^2 + 2^3 + ...+2^(n-1) = 2^n - 1 Homework Equations Sum formula? 3. The Attempt at a Solution I know you are suppose to use the base case and prove its true for k +1, but I'm not sure what to do for similar bases. Can someone please solve it step by step? Thanks!
  49. M

    Do I Need All Three Math Textbooks by Ron Larson?

    https://www.amazon.com/dp/1133949010/?tag=pfamazon01-20 https://www.amazon.com/dp/1285057090/?tag=pfamazon01-20 https://www.amazon.com/dp/1133959741/?tag=pfamazon01-20 So I'm planning on buying the books in the links above (Algebra and trig, precalc and calc by Ron Larson), but as they are...
  50. Ritzycat

    Precalculus topics necessary for Calculus

    Hello. I'm a high school senior, currently taking a Pre-Calculus class. I am having little trouble understanding the material and I feel the class moves too slowly for my liking. I want to learn more outside of class on my own, but I don't want to be learning Algebra review. I have heard from...
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