Free ebook · Mathematics
Trig identities either click or they never do. Most resources make it worse.
They dump formulas without context, skip the proofs that would make them stick, and bury the useful parts under complexity. This free 73-page guide derives every identity, builds each concept on the last, and ends with quick-reference tables for exam recall.
Free PDF · 73 pages · works on any device · no payment at checkout
Format:
Why this guide
A formula you memorized blindly is a formula you will forget mid-exam.
The difference between recalling an identity and reconstructing one is the derivation. This guide never hands you one without the other.
How trig usually gets taught
the default- Formulas dumped without context, in one intimidating sheet
- Proofs skipped, exactly the ones that would help you understand
- Useful content buried under unnecessary complexity
- Memorize and hope is the implied study strategy
How this guide does it
this guide- Every identity derived. You see where each formula comes from
- Concepts build in order, from the unit circle up through Euler’s formula
- Worked examples show exactly how to apply each formula
- Quick-reference tables at the end, so recall is a page-flip, not a 70-page hunt
What’s inside
Eight parts and 23 chapters, from the unit circle to Euler.
If you can solve basic algebra problems, you have enough background for chapter one. Everything after that is built in front of you.
I. Foundations
- The unit circle and degree-radian conversion
- All six trig functions, defined clearly
- The special angle table you will reference constantly
II. Fundamental identities
- Reciprocal, ratio, and even-odd identities
- Each Pythagorean identity with a full proof
III. Sum, difference, multiple angles
- Sum and difference formulas for sine, cosine, tangent
- Double angles, all three forms of cos 2θ
- Half angles with sign determination, plus triple angles
IV. Product and sum
- Product-to-sum and sum-to-product conversions
- The derivations that show up in calculus integration constantly
V. Cofunction and periodicity
- Complementary and supplementary angles
- The reference angle method for any quadrant
VI. Triangle laws
- Law of Sines, Law of Cosines, Law of Tangents
- Area formulas including Heron’s formula
- Beyond right triangles, to any triangle problem
VII. Advanced topics
- Inverse trig and hyperbolic functions
- Euler’s formula, the bridge to calculus and complex analysis
VIII. Applications and practice
- Strategies for proving identities
- Derivatives and integrals of trig functions
- Wave motion, harmonic oscillation, AC circuits
Quick-reference tables
- Every major identity consolidated into scannable tables
- Print them. Keep them next to your desk during problem sets
73 pages, 23 chapters, every identity with its derivation and worked examples.
Who this is for
Written for four kinds of readers.
Board, JEE, and competitive exam students
High school students who need the identities cold under time pressure, with the tables for last-week revision.
Engineering, physics, and math undergrads
The identities keep showing up in calculus and circuits. The derivations here are the ones your course assumes you remember.
Self-learners
A structured reference that doesn’t assume prior knowledge. Basic algebra is enough background to start.
Teachers and tutors
A well-organized resource for lesson planning, with proofs and worked examples already laid out in teaching order.
Look inside the book.
Preview the writing, structure, and page layout before you decide.
Get the guide
Trigonometric Identities
Free
PDF · 73 pages · works on any device
- All 23 chapters, from the unit circle to Euler’s formula and hyperbolic functions
- Every identity with its derivation, not just the formula
- Worked examples showing exactly how to apply each formula
- Practice problems with answers
- Quick-reference tables that consolidate every major identity
- Clean mathematical typesetting with clear diagrams
No payment. Checkout creates your download link instantly.
Questions students ask
Asked before downloading, answered straight.
Is it actually free?
Yes. There’s no payment step. The checkout exists only to create your download link, and it does that instantly.
What background do I need?
If you can solve basic algebra problems, you have enough to start. The guide builds from the unit circle and right triangle definitions up through Euler’s formula and hyperbolic functions.
Why derivations instead of a formula sheet?
Because a memorized formula fades and a derived one can be rebuilt at the desk. The quick-reference tables at the end handle recall. The derivations handle understanding. You need both in an exam.
Does it include practice, or just theory?
Both. Worked examples for every formula, practice problems with answers, and strategies for proving identities in Part VIII.
Will it help with calculus?
That’s a design goal. The product-to-sum conversions show up in integration problems constantly, and Part VIII covers derivatives and integrals of trig functions directly.
Do I have to read all 73 pages?
No. It’s built so you won’t hunt through 70 pages for one formula: the final pages consolidate every major identity into scannable tables you can print and keep next to your desk.
What I’m not going to claim
This guide has no ratings yet, and I’d rather tell you that than dress the page up with invented praise. It’s free, so trying it costs you nothing but the download.
I’m also not going to claim 73 pages will do the practice for you. The derivations make the identities make sense. Making them permanent still takes problem sets, which is why the practice problems come with answers and the tables are meant to be printed, not admired.
Hey, I’m Gaurav 👋
I’ve been writing mathematics for students since 2008, and trig identities are the topic I’ve watched defeat the most capable people, almost always because someone handed them a formula sheet instead of a derivation. This guide is the version I wish someone had handed me.
The numbers, since you probably won’t read a full bio:
- 18 years building on the web, and a WordPress core contributor
- 2,000+ articles published since 2008, a lot of them math explainers like this one
- 850+ clients shipped in that time, from study notes to software
Before your next problem set
Stop memorizing blindly. Start deriving.
73 pages, every identity with its proof, and printable tables for the night before the exam. Free, with the link issued the moment you check out.
Free PDF · 73 pages · no payment at checkout