trigonometry
The Pythagorean identity is just Pythagoras, divided
sin²α + cos²α = 1 is not a new fact to memorise. It is the Pythagorean theorem with both sides divided by c² — and two more useful identities fall straight out of it.
ACE MATH · Foundations Series
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Printable math study guides with every step written out: twenty volumes, from logic and sets, over functions and relations to differential equations. High school and university level, for students and teachers alike.
- 20volumes
- 1,298worked examples
- 2,045practice problems
- 3,111printable pages
In every volume
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1 · Study guide
The theory, every formula derived, and worked examples with every step written out. Split into parts you can print one at a time.
2 · Practice workbook
Problems for every lesson, with a complete answer key at the back.
3 · Formula reference
Every formula of the volume on a few pages, to keep beside you while you work.
The Foundations Series
See every guide →- ILogic and SetsHigh School$14.99
- IIReal NumbersHigh School$14.99
- IIIProportion and PercentageHigh School$14.99
- IVIntroduction to GeometryHigh School$19.99
- VPowers, Roots and Complex NumbersHigh School$14.99
- VIQuadratic Equations and FunctionsHigh School$19.99
- VIIExponential and Logarithmic FunctionsHigh School$14.99
- VIIITrigonometryHigh School$19.99
- IXPlane and Solid GeometryHigh School$19.99
- XMatrices, Determinants and VectorsHigh School + University$19.99
- XIAnalytic Geometry in the PlaneHigh School$19.99
- XIISequences, Limits and InductionHigh School + University$19.99
- XIIIPolynomials and Complex NumbersHigh School$19.99
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- XVDerivativesHigh School + University$24.99
- XVICurve SketchingHigh School + University$24.99
- XVIIIntegralsHigh School + University$24.99
- XVIIIMultiple, Line and Surface IntegralsUniversity$24.99
- XIXDifferential EquationsHigh School + University$24.99
- XXSeriesUniversity$19.99
Written by Jovana
I graduated in mathematics, then I taught it: as a teacher in a classroom and as a tutor in one-as-one sessions. These guides are the result of years of experience, and they are designed to help you learn math in the most effective way possible.
Free lessons
All lessons →trigonometry
The three special angles, from two triangles
Where the exact values of sin, cos and tan at 30°, 45° and 60° come from — derived from half an equilateral triangle and half a square, not memorised.
trigonometry
Radians: why 180° = π, and what a radian actually is
A radian is not a conversion factor to memorise — it is the angle standing on an arc as long as the radius. Everything else follows from one line.
Free download
The trigonometry formula sheet
Every trigonometry formula on nine printable pages: exact values, the reduction rules, every identity, and a full-page unit circle chart. No sign-up, just the PDF.
Download the PDF