About Us

Why Choose StudyPug

How it works

Pricing

Testimonials

Contact Us

Blog

Basic Math

Algebra

Geometry

Trigonometry

Calculus

Linear Algebra

Differential Equations

Statistics

Chemistry

Organic Chemistry

Physics

Microeconomics

For Students

For Parents

For Home Schoolers

For Teachers

Australia

Canada

Ireland

New Zealand

Singapore

United Kingdom

United States

Sitemap

Terms of Service

Privacy Policy

Accessibility

How to use double-angle identities

Precalculus: Master Advanced Math Concepts

Functions

One to one functions

Identifying functions

Introduction to linear equations

auto-gen

Function notation

Composite functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Operations of Functions – In a Nutshell

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Even and odd functions

Difference quotient: applications of functions

Polynomials

Descartes&apos; rule of signs

Descartes' Rule of Signs

Descartes' rule of signs

Descartes" rule of signs

Polynomial long division

Polynomial synthetic division

Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

Binomial theorem

What is a polynomial function?

Polynomial functions

Recognizing a Polynomial Function

Factor theorem

Using the Factor Theorem to Test For Factors of a Polynomial

Rational zero theorem

Rational Zero Theorem

Characteristics of polynomial graphs

Determining the equation of a polynomial function

Applications of polynomial functions

Multiplicities of polynomials

Imaginary zeros of polynomials

Solving polynomial inequalities

Rational Functions

What is a rational function?

Point of discontinuity

Slant asymptote

Determining the Equation of a Slant Asymptote Using Long Division

Determining the Equation of a Slant Asymptote Using Synthetic Division

Solving rational inequalities

Solving Rational Inequalities With Two Fractions

Vertical asymptote

Horizontal asymptote

Horizontal Asymptote

Graphs of rational functions

Radical

Transformations of radical functions

Square root of a function

Solving radical equations

Solving Radical Equations Involving One Square Root Term

Solving Radical Equations Involving More than One Square Root Term

Basic radical functions

Basic Radical Function

Basic Radical Functions

Roots and Rational Exponents

Evaluating and simplifying radicals

Power of a power rule

Simplify the power

Combining the exponent rules

Rational exponents

Convert between radicals and rational exponents

Square and square roots

Square Root of a Perfect Square

Converting radicals to mixed radicals

Converting radicals to entire radicals

Systems of Equations

Solving 3 variable systems of equations by substitution

Solving 3 variable systems of equations by elimination

Word problems relating 3 variable systems of equations

Solving 3 variable systems of equations with no or infinite solutions

Solving 3 variable systems of equations (no solution, infinite solutions)

System of Equations With No Solution

System of Equations With Infinite Solutions

System of Equations With Infinite Solutions - Extended

Determining number of solutions to linear equations

Solving linear systems by graphing

Solving systems of linear equations by graphing

Using elimination method to solve systems of equations

Solving systems of linear equations by elimination

Using substitution method to solve systems of equations

Solving systems of linear equations by substitution

System of Inequalities

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

Shortcut: The vertex formula

Shortcut: Vertex formula

Converting general form into vertex form by applying the vertex formula

Vertex Formula Application

Solving absolute value inequalities

Solving Absolute Value Inequalities Involving "less than"

Solving Absolute Value Inequalities Involving "greater than"

Recognizing Absolute Value Inequalities with "No Solution" or "All Real Numbers"

Graphing linear inequalities in two variables

Graphing quadratic inequalities in two variables 

Unit circle

Quotient identities and reciprocal identities

Pythagorean identities

Sum and difference identities

Sum and Difference Identities

Double-angle identities

Use sine ratio to calculate angles and side (Sin = \( \frac{o}{h}\) )

Use cosine ratio to calculate angles and side (Cos = \( \frac{a}{h}\) )

Combination of SohCahToa questions

Word problems relating ladder in trigonometry

Word problems relating guy wire in trigonometry

Use tangent ratio to calculate angles and side (Tan = \( \frac{o}{a}\) )

Solving first degree trigonometric equations

Law of sines

Ambiguous case: SSA triangles

Law of cosines

Angle in standard position

Coterminal angles

Coterminal Angles

Reference angle

Find the exact value of trigonometric ratios

ASTC rule in trigonometry (All Students Take Calculus)

ASTC rule in trigonometry

ASTC rule in trigonometry (All Students Take Calculus)

Converting between degrees and radians

Trigonometric ratios for angles in radians

Trigonometric ratios of angles in radians

Radian measure and arc length

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Cotangent graph: y = cot x

Secant graph: y = sec x

Cosecant graph: y = csc x

Graphing transformations of trigonometric functions

Determining trigonometric functions given their graphs

Determining non-permissible values for trig expressions

Sequences and Series

Arithmetic sequences

Arithmetic series

Arithmetic series formula

Geometric sequences

Geometric Series

Geometric series

Infinite geometric series

Sigma notation

Influencing factors in data collection

Median and mode

Median and Mode Table

Median and Mode – Word Problem

Median of an even length list

Median of an odd length list

Mean

Mean Word Problems

Find the Mean

Get better math marks with our complete Precalculus help &ndash; be it Precalculus <a href="http://www.corestandards.org/Math/">Common Core Standards</a>, or <a href="https://clep.collegeboard.org/science-and-mathematics/precalculus">CLEP Precalculus</a>. We've got you covered!
Just like your class or textbook, our complete help for Pre calculus includes topics such as Factoring trinomials, Simplifying exponents, <a href="https://www.studypug.com/pre-calculus/unit-circle">Unit circle</a>, <a href="https://www.studypug.com/pre-calculus/introduction-to-vectors">Vectors</a>, <a href="https://www.studypug.com/pre-calculus/introduction-to-imaginary-numbers">Complex numbers</a>, <a href="https://www.studypug.com/pre-calculus/finding-inverse-trigonometric-function-from-its-graph">Inverse functions</a>, <a href="https://www.studypug.com/pre-calculus/convert-from-logarithmic-to-exponential-form">Logarithmic functions</a>, and more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest precalculus problems. Then, strengthen your understanding with tons of <a href="https://www.studypug.com/pre-calculus">precalculus practice</a>. 
All our lessons are taught by experienced <a href="https://www.studypug.com/pre-calculus-tutor">Precalculus tutors</a>. Let&apos;s finish your homework in no time, and ACE that final.

Precalculus

math

<h2>What is <a href="https://www.studypug.com/pre-calculus">Precalculus</a>?</h2>
Precalculus is a course that covers the more complex elements of both <a href="https://www.studypug.com/algebra-help">algebra</a> and <a href="https://www.studypug.com/trigonometry">trigonometry</a>, elements that were not necessarily explored in depth in your previous trig or algebra courses. For example, you&apos;ll dive deeper into topics like polynomial synthetic divisions, the transformation of functions, determinants and inverses of matrices, and much more.
Prerequisites for the course would be either <a href="https://www.studypug.com/algebra-2">Algebra 2 course</a> or <a href="https://www.studypug.com/geometry">Geometry course</a>. Upon completing the course, students would be better prepared to undertake lessons in <a href="https://www.studypug.com/calculus">Calculus</a>.
For the most part, courses will cover standard content like functions and function composition, as well as inverse functions in relation to sets and real numbers. Outside of these topics, the course content may vary depending on the nature of the course. For example, some courses may have an emphasis on preparing students for careers within the business world, meaning that the course content has more of a focus on topics like power functions and matrices.
Regardless of your individual course content, our vast collection of <a href="https://www.studypug.com/pre-calculus">precalculus help</a>
lessons will cover everything you need. We&apos;ve worked to ensure that our videos cover all the topics you&apos;d expect to find in the classroom and within modern textbooks. In addition, our videos offer step-by-step examples that, unlike the classroom, can be paused, rewound, or fast-forwarded, allowing you to learn at your own pace.

<h2>Is Precalculus Hard?</h2>
As mentioned above, precalculus explores areas of trigonometry and algebra in greater depth than in your previous courses. With that in mind, it's essential that you have a solid foundation of knowledge in trigonometry and algebra to build upon. Failing to do so will make precalculus a much tougher challenge than it needs to be.
If you feel like you need to broaden your understanding of trig and algebra before attempting precalculus, or if you are already in classes and find that it&apos;s becoming a bit of a struggle, you&apos;re not alone. We have many students like you who are using our platform to get <a href="https://www.studypug.com/pre-calculus">pre cal help</a> to tackle tricky precalculus problems and prepare for their upcoming exams.
You can start with our <a href="https://www.studypug.com/algebra-2-tutor">algebra 2 tutorials</a> and <a href="https://www.studypug.com/trigonometry-tutor">trigonometry tutorials</a> to further build your basic knowledge or jump straight into our online <a href="https://www.studypug.com/pre-calculus">precalc help</a>. As a subscriber, you&apos;ll have access to every video on our site, providing you with math guides whenever you need them. Regardless of the topic you need help with, our videos will break down the information into bite sized chunks, making them easier to digest and retain. We cover all the aspects of precalculus that are bound to come up in your exams, so whatever area you need help mastering, we&apos;ve got the content that can help you succeed!

<h2>How to Pass Precalculus?</h2>
If you want to successfully pass your precalculus test, you should revise, revise, revise! That cannot be stressed enough, the best way to learn is with repetition. Review what you&apos;ve been taught in the classroom and build effective study sessions to retain that information. Give yourself some time to assess your work and use our easy practice materials to help you highlight any areas of weakness that you may have.
Getting yourself into a good study habit of completing practice papers and sitting mock exams will help to build your confidence ahead of sitting your actual precalculus paper. Work within the time constraints of each paper and have someone else mark your tests for you. Reviewing your performance and tracking your improvement within your weaker areas, will show you that revision actually works and will encourage you to stick with it!
We at StudyPug, understand that getting yourself into the study mood can be difficult at times. We also know that many students find it boring to work from a textbook. That&apos;s why we offer an extensive collection of fun and easy to follow <a href="https://www.studypug.com/pre-calculus-tutor">precalculus video tutorials</a> that manage to deliver the same precalculus textbook answers, but in a much more conversational way that's easier to understand.
Put simply, to improve your chances of passing precalculus, you&apos;ll need to spend a good amount of time revising and you should utilize StudyPug&apos;s vast collection of content to get the most out of your revision time. We&apos;ll not only get you prepared for your exams, but we can also help you perform better in class. If there&apos;s something in your lesson that you couldn&apos;t make sense of, jump online and browse our content. We&apos;ll have video tutorials on the subject that can help clear up any confusion you have. Think of us as your <a href="https://www.studypug.com/pre-calculus-tutor">online precalculus tutor</a>, available whenever you need us, and at the fraction of the cost of a personal tutor.

<h2>PreCalculus Vs. Algebra</h2>
Elements of algebra make up certain sections of precalculus, which is why a prerequisite for most courses is a qualification in algebra 1 and algebra 2. These courses complement the content of precalculus courses and are used as the building blocks from which you will develop your understanding of the more complex elements of precalculus. To that end, precalculus is slightly more complicated and trickier than basic algebra. Learn that first and precalculus becomes easier to understand.

<h2>Teach Me Precalculus!</h2>
If you&apos;re looking for precalculus tutorial videos, you&apos;re in the right place! We offer <a href="https://www.studypug.com/math-tutor/">free math tutor online 24/7</a> help and have 1000s of lessons across a variety of mathematical topics, including trig, algebra, and content for <a href="https://www.studypug.com/pre-calculus">precalculus homework help</a>. If you&apos;re struggling with unit circles, vectors, conic sections, polynomials, or anything else, we can help!
We&apos;re well aware that the way you learn may not be the same as everybody else and that&apos;s why we have built a platform with a "precalculus for beginners" approach that starts from the ground up, assumes no prior knowledge, and acts as a fantastic intro to calculus. Each section of our content has also been designed to flow naturally from one topic to the next, ensuring that you can build off what you&apos;ve just learned, introducing more complex elements when you&apos;re ready.
To get you started with your precalculus exam prep, we&apos;re offering a collection of <a href="https://www.studypug.com/math-tutor/">free math tutor</a> precalculus lessons across the following subject areas:
<ul type="disc">
<li><a href="https://www.studypug.com/pre-calculus/composite-functions">Composite Functions</a></li>
<li><a href="https://www.studypug.com/pre-calculus/reflection-across-the-y-axis">Reflection Across the Y-axis</a></li>
<li><a href="https://www.studypug.com/pre-calculus/long-division-of-polynomial-functions">Polynomial Long Division</a></li>
<li><a href="https://www.studypug.com/pre-calculus/convert-from-logarithmic-to-exponential-form">Converting from Logarithmic Form to Exponential Form</a></li>
<li><a href="https://www.studypug.com/pre-calculus/exponent-power-rule">Exponents: Power Rule</a></li>
<li><a href="https://www.studypug.com/pre-calculus/shortcut-vertex-formula">Shortcut Vertex Formula</a></li>
<li>And Many More!</li>
</ul>
Browse them all today and see how we can make precalculus much easier to understand.
It&apos;s worth noting that having a firm grip on precalculus can greatly impact your career success. There&apos;s a great amount of <a href="https://www.studypug.com/blog/6-high-paid-careers-for-people-who-are-good-at-math/">high paying jobs for people that are good at math</a>. So get studying!

<h2>Compatible Precalculus Textbooks</h2>
We know that students who want to succeed may need revision guides to help them. We also know that not everyone can afford the expensive textbooks. To that end, our precalculus content has been thoughtfully created by expert math teachers to ensure that our content covers all the topics you&apos;d expect to find in the following textbooks.
<ul type="disc">
<li>Slader - Precalculus</li>
<li>Precalculus with Limits</li>
<li>Larson precalculus with Limits</li>
<li>Precalculus for Dummies</li>
<li>Larson - Precalculus with Limits</li>
<li>Glencoe - Precalculus</li>
<li>Precalculus &ndash; Michael Sullivan</li>
<li>Precalculus with limits a graphing approach pdf</li>
<li>Precalculus Mathematics for Calculus 7th Edition</li>
<li>Blitzer - Precalculus (textbook)</li>
<li>Precalculus: Graphical, Numerical, Algebraic</li>
</ul>
Essentially, we&apos;ve taken the same information found within each of these books and combined them into one subscription, granting you unlimited access to a vast range of video content. When it comes to precalculus lessons and revision guides, StudyPug is all you need.
We find that a lot of our students prefer the video format as the content is delivered in a conversational way that&apos;s easier to follow than traditional textbooks. Read our precalculus reviews from our loyal base of customers who also needed <a href="https://www.studypug.com/pre-calculus">help with precalculus</a> and see how we've managed to help students just like you succeed in their precalculus exams

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-precalculus.png

Double-angle identities

What You'll Learn

Apply sine, cosine, and tangent double-angle formulas to simplify trigonometric expressions

Identify which cosine 2θ formula to use based on expression structure

Convert complex trigonometric expressions using double-angle identities

Verify factored trigonometric results by applying quotient and reciprocal identities

What You'll Practice

Simplifying expressions using sin(2θ) = 2sin(θ)cos(θ)

Selecting among three cos(2θ) formulas to cancel terms

Proving trigonometric identities with double-angle formulas

Finding exact values of double-angle expressions from given ratios

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

10 Video lessons

Practice exercises

Learning resources

Skills

Double-Angle Identities

Trigonometric Identities

Simplification

Factoring

Quotient Identities

Reference Angles

Proof Techniques