## 17Calculus - Precalculus

### Functions

Functions

Polynomials

Rational Functions

Matrices

Systems

Trigonometry

Complex Numbers

### Practice

Calculus 1 Practice

Calculus 2 Practice

Practice Exams

### Articles

NEW for 2020 - We have recently expanded the precalculus section with hundreds more practice problems and several new pages as well as expanded discussion on many more pages.

There are lots and lots of online videos and websites to help you review and learn precalculus and college algebra. And you could waste a lot of time trying to find help.

So, how can you prepare for calculus and not waste time?

Use 17Calculus Precalculus

We have sorted through lots of videos and websites for you and organized everything you need. We build discussion around videos and provide lots of practice problems, ALL with worked out solutions (not just answers but complete, worked out in detail and explained solutions).

So, who is this site for? We built this site for the serious college student in math, engineering, science and/or business . . . pretty much any college student serious about learning precalculus, college algebra, algebra 2, analytic geometry or trigonometry. We also assume that you will be going on to calculus but this is not a requirement to learning from this site.

To get the most out of this site, you need a solid background in basic algebra and basic geometry. You also need some exposure to trigonometry, although we cover some of the basics.

So how much will this cost you? Nothing! All the material is free.

Ready to really UNDERSTAND precalculus? Okay, let's go.

To get started, select a topic from the menu.

Precalculus Books Recommendations

Here are a few books that we recommend from which to learn precalculus. For a complete list of books and to read about how to get the most out of your textbooks and supplementary books, go to our college books page.

Precalculus
Demystified
Schaums Outline of Precalculus
Larson
Precalculus

Really UNDERSTAND Precalculus

### Trig Formulas

The Unit Circle

The Unit Circle [wikipedia]

Basic Trig Identities

Set 1 - basic identities

$$\displaystyle{ \tan(t) = \frac{\sin(t)}{\cos(t)} }$$

$$\displaystyle{ \cot(t) = \frac{\cos(t)}{\sin(t)} }$$

$$\displaystyle{ \sec(t) = \frac{1}{\cos(t)} }$$

$$\displaystyle{ \csc(t) = \frac{1}{\sin(t)} }$$

Set 2 - squared identities

$$\sin^2t + \cos^2t = 1$$

$$1 + \tan^2t = \sec^2t$$

$$1 + \cot^2t = \csc^2t$$

Set 3 - double-angle formulas

$$\sin(2t) = 2\sin(t)\cos(t)$$

$$\displaystyle{ \cos(2t) = \cos^2(t) - \sin^2(t) }$$

Set 4 - half-angle formulas

$$\displaystyle{ \sin^2(t) = \frac{1-\cos(2t)}{2} }$$

$$\displaystyle{ \cos^2(t) = \frac{1+\cos(2t)}{2} }$$

Trig Derivatives

 $$\displaystyle{ \frac{d[\sin(t)]}{dt} = \cos(t) }$$ $$\displaystyle{ \frac{d[\cos(t)]}{dt} = -\sin(t) }$$ $$\displaystyle{ \frac{d[\tan(t)]}{dt} = \sec^2(t) }$$ $$\displaystyle{ \frac{d[\cot(t)]}{dt} = -\csc^2(t) }$$ $$\displaystyle{ \frac{d[\sec(t)]}{dt} = \sec(t)\tan(t) }$$ $$\displaystyle{ \frac{d[\csc(t)]}{dt} = -\csc(t)\cot(t) }$$

Inverse Trig Derivatives

 $$\displaystyle{ \frac{d[\arcsin(t)]}{dt} = \frac{1}{\sqrt{1-t^2}} }$$ $$\displaystyle{ \frac{d[\arccos(t)]}{dt} = -\frac{1}{\sqrt{1-t^2}} }$$ $$\displaystyle{ \frac{d[\arctan(t)]}{dt} = \frac{1}{1+t^2} }$$ $$\displaystyle{ \frac{d[\arccot(t)]}{dt} = -\frac{1}{1+t^2} }$$ $$\displaystyle{ \frac{d[\arcsec(t)]}{dt} = \frac{1}{\abs{t}\sqrt{t^2 -1}} }$$ $$\displaystyle{ \frac{d[\arccsc(t)]}{dt} = -\frac{1}{\abs{t}\sqrt{t^2 -1}} }$$

Trig Integrals

 $$\int{\sin(x)~dx} = -\cos(x)+C$$ $$\int{\cos(x)~dx} = \sin(x)+C$$ $$\int{\tan(x)~dx} = -\ln\abs{\cos(x)}+C$$ $$\int{\cot(x)~dx} = \ln\abs{\sin(x)}+C$$ $$\int{\sec(x)~dx} =$$ $$\ln\abs{\sec(x)+\tan(x)}+C$$ $$\int{\csc(x)~dx} =$$ $$-\ln\abs{\csc(x)+\cot(x)}+C$$

### Topics Listed Alphabetically

Single Variable Calculus

Multi-Variable Calculus

Differential Equations

Precalculus

Engineering

Circuits

Semiconductors

### Search Practice Problems

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