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© 2026 Physics Playground. Feito para os curiosos.Idioma

Preface
1Functions
2Linear Functions
3Polynomial and Rational Functions
4Exponential and Logarithmic Functions
5Trigonometric Functions
6Periodic Functions
7Trigonometric Identities and Equations
8Further Applications of Trigonometry
9Systems of Equations and Inequalities
10Analytic Geometry
11Sequences, Probability and Counting Theory
12Introduction to Calculus
ABasic Functions and Identities
Answer Key
Index

Biblioteca Precalculus

Sumário

Preface
1Functions
2Linear Functions
3Polynomial and Rational Functions
4Exponential and Logarithmic Functions
5Trigonometric Functions
6Periodic Functions
7Trigonometric Identities and Equations
8Further Applications of Trigonometry
9Systems of Equations and Inequalities
10Analytic Geometry
11Sequences, Probability and Counting Theory
12Introduction to Calculus
ABasic Functions and Identities
Answer Key
Index

Key Equations

Key Equations

Pythagorean Identities	$\begin{array}{l} \sin^{2} θ + \cos^{2} θ = 1 \\ 1 + \cot^{2} θ = \csc^{2} θ \\ 1 + \tan^{2} θ = \sec^{2} θ \end{array} \begin{array}{l} \sin^{2} θ + \cos^{2} θ = 1 \\ 1 + \cot^{2} θ = \csc^{2} θ \\ 1 + \tan^{2} θ = \sec^{2} θ \end{array}$
Even-odd identities	$\begin{array}{l} \tan (- θ) = - \tan θ \\ \cot (- θ) = - \cot θ \\ \sin (- θ) = - \sin θ \\ \csc (- θ) = - \csc θ \\ \cos (- θ) = \cos θ \\ \sec (- θ) = \sec θ \end{array} \begin{array}{l} \tan (- θ) = - \tan \\ \cot (- θ) = - \cot \\ \sin (- θ) = - \sin \\ \csc (- θ) = - \csc \\ \cos (- θ) = \cos \\ \sec (- θ) = \sec \end{array}$
Reciprocal identities	$\begin{array}{l} \sin θ = \frac{1}{\csc θ} \\ \cos θ = \frac{1}{\sec θ} \\ \tan θ = \frac{1}{\cot θ} \\ \csc θ = \frac{1}{\sin θ} \\ \sec θ = \frac{1}{\cos θ} \\ \cot θ = \frac{1}{\tan θ} \end{array} \begin{array}{l} \sin \\ \cos \\ \tan \\ \csc \\ \sec \\ \cot \end{array}$
Quotient identities	$\begin{array}{l} \tan θ = \frac{\sin θ}{\cos θ} \\ \cot θ = \frac{\cos θ}{\sin θ} \end{array} \begin{array}{l} \tan \\ \cot \end{array}$

Sum Formula for Cosine	$\cos (α + β) = \cos α \cos β - \sin α \sin β \cos (α + β) = \cos$
Difference Formula for Cosine	$\cos (α - β) = \cos α \cos β + \sin α \sin β \cos (α - β) = \cos$
Sum Formula for Sine	$\sin (α + β) = \sin α \cos β + \cos α \sin β \sin (α + β) = \sin$
Difference Formula for Sine	$\sin (α - β) = \sin α \cos β - \cos α \sin β \sin (α - β) = \sin$
Sum Formula for Tangent	$\tan (α + β) = \frac{\tan α + \tan β}{1 - \tan α \tan β} \tan (α + β) = \frac{\tan}{1 - \tan}$
Difference Formula for Tangent	$\tan (α - β) = \frac{\tan α - \tan β}{1 + \tan α \tan β} \tan (α - β) = \frac{\tan}{1 + \tan}$
Cofunction identities	$\begin{array}{l} \sin θ = \cos (\frac{π}{2} - θ) \\ \cos θ = \sin (\frac{π}{2} - θ) \\ \tan θ = \cot (\frac{π}{2} - θ) \\ \cot θ = \tan (\frac{π}{2} - θ) \\ \sec θ = \csc (\frac{π}{2} - θ) \\ \csc θ = \sec (\frac{π}{2} - θ) \end{array} \begin{array}{l} \sin \\ \cos \\ \tan \\ \cot \\ \sec \\ \csc \end{array}$

Double-angle formulas	$\begin{array}{l} \sin (2 θ) = 2 \sin θ \cos θ \\ \cos (2 θ) = \cos^{2} θ - \sin^{2} θ \\ = 1 - 2 \sin^{2} θ \\ = 2 \cos^{2} θ - 1 \\ \tan (2 θ) = \frac{2 \tan θ}{1 - \tan^{2} θ} \end{array} \begin{array}{l} \sin (2 θ) = 2 \sin \\ \cos (2 θ) = \cos^{2} θ - \sin^{2} θ \\ = 1 - 2 \sin^{2} θ \\ = 2 \cos^{2} θ - 1 \\ \tan (2 θ) = \frac{2 \tan}{1 - \tan^{2} θ} \end{array}$
Reduction formulas	$\begin{array}{l} \sin^{2} θ = \frac{1 - \cos (2 θ)}{2} \\ \cos^{2} θ = \frac{1 + \cos (2 θ)}{2} \\ \tan^{2} θ = \frac{1 - \cos (2 θ)}{1 + \cos (2 θ)} \end{array} \begin{array}{l} \sin^{2} θ = \frac{1 - \cos (2 θ)}{2} \\ \cos^{2} θ = \frac{1 + \cos (2 θ)}{2} \\ \tan^{2} θ = \frac{1 - \cos (2 θ)}{1 + \cos (2 θ)} \end{array}$
Half-angle formulas	$\begin{array}{l} \sin \frac{α}{2} = \pm \sqrt{\frac{1 - \cos α}{2}} \\ \cos \frac{α}{2} = \pm \sqrt{\frac{1 + \cos α}{2}} \\ \tan \frac{α}{2} = \pm \sqrt{\frac{1 - \cos α}{1 + \cos α}} \\ = \frac{\sin α}{1 + \cos α} \\ = \frac{1 - \cos α}{\sin α} \end{array} \begin{array}{l} \sin \\ \cos \\ \tan \\ = \frac{\sin}{1 + \cos} \\ = \frac{1 - \cos}{\sin} \end{array}$

Product-to-sum Formulas	$\begin{array}{l} \cos α \cos β = \frac{1}{2} [\cos (α - β) + \cos (α + β)] \\ \sin α \cos β = \frac{1}{2} [\sin (α + β) + \sin (α - β)] \\ \sin α \sin β = \frac{1}{2} [\cos (α - β) - \cos (α + β)] \\ \cos α \sin β = \frac{1}{2} [\sin (α + β) - \sin (α - β)] \end{array} \begin{array}{l} \cos \\ \sin \\ \sin \\ \cos \end{array}$
Sum-to-product Formulas	$\begin{array}{l} \sin α + \sin β = 2 \sin (\frac{α + β}{2}) \cos (\frac{α - β}{2}) \\ \sin α - \sin β = 2 \sin (\frac{α - β}{2}) \cos (\frac{α + β}{2}) \\ \cos α - \cos β = - 2 \sin (\frac{α + β}{2}) \sin (\frac{α - β}{2}) \\ \cos α + \cos β = 2 \cos (\frac{α + β}{2}) \cos (\frac{α - β}{2}) \end{array} \begin{array}{l} \sin \\ \sin \\ \cos \\ \cos \end{array}$

Standard form of sinusoidal equation	$y = A \sin (B t - C) + D or y = A \cos (B t - C) + D y = A$
Simple harmonic motion	$d = a \cos (ω t) or d = a \sin (ω t) d = a$
Damped harmonic motion	$f (t) = a e^{- c}^{t} \sin (ω t) or f (t) = a e^{- c t} \cos (ω t) f (t) = a e^{- c} t \sin (ω t)$

Key Equations

Key Equations

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

Zeros of Polynomial Functions

Zeros of Polynomial Functions

3.7Rational Functions

3.7Rational Functions

3.8Inverses and Radical Functions

3.8Inverses and Radical Functions

3.9Modeling Using Variation

3.9Modeling Using Variation

Chapter Review

Key Terms
Key Equations
Key Concepts

Chapter Review

Key Terms
Key Equations
Key Concepts

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

4.6

4.6

Exponential and Logarithmic Equations

Exponential and Logarithmic Equations

4.7Exponential and Logarithmic Models

4.7Exponential and Logarithmic Models

4.8Fitting Exponential Models to Data

4.8Fitting Exponential Models to Data

Chapter Review

Key Terms
Key Equations
Key Concepts

Chapter Review

Key Terms
Key Equations
Key Concepts

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

Key Concepts

Key Concepts

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

7.6

7.6

Modeling with Trigonometric Functions

Modeling with Trigonometric Functions

Chapter Review

Key Terms
Key Equations
Key Concepts

Chapter Review

Key Terms
Key Equations
Key Concepts

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

8.6

8.6

Parametric Equations

Parametric Equations

8.7Parametric Equations: Graphs

8.7Parametric Equations: Graphs

Chapter Review

Key Terms
Key Equations
Key Concepts

Chapter Review

Key Terms
Key Equations
Key Concepts

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

9.6

9.6

Solving Systems with Gaussian Elimination

Solving Systems with Gaussian Elimination

9.7Solving Systems with Inverses

9.7Solving Systems with Inverses

9.8Solving Systems with Cramer's Rule

9.8Solving Systems with Cramer's Rule

Chapter Review

Key Terms
Key Equations
Key Concepts

Chapter Review

Key Terms
Key Equations
Key Concepts

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

Key Terms

Key Terms

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

11.6

11.6

Binomial Theorem

Binomial Theorem

11.7Probability

11.7Probability

Chapter Review

Key Terms
Key Equations
Key Concepts

Chapter Review

Key Terms
Key Equations
Key Concepts

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

Key Equations

Key Equations

Exercises

Review Exercises
Practice Test

Exercises

Review Exercises
Practice Test

Chapter 9

Chapter 9

AnteriorKey Terms Próxima Key Concepts

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