SinCosTan
The Journal
How to Solve a Right Triangle
A step-by-step method for finding every unknown side and angle in a right triangle using the trig ratios, inverse functions, and the Pythagorean theorem.
SOHCAHTOA Explained: The Trig Ratios Made Simple
SOHCAHTOA is a six-letter memory trick that hands you the three core trig ratios, and this guide shows what each piece means with a worked example.
Law of Sines vs Law of Cosines: Which One to Use
A practical guide to choosing between the Law of Sines and the Law of Cosines, with the deciding rules and two short worked examples using real numbers.
Reading the Unit Circle
A guided tour of the unit circle, showing why each point is (cos, sin), listing the key angles and their exact values, and explaining the quadrant signs.
What Are Radians, and Why Mathematicians Prefer Them
Radians are the circle's own natural angle unit, and this article defines them from arc length, shows both conversions, and explains why calculus insists on them.
Graphing Sine and Cosine Waves
Learn to read amplitude, period, phase shift, and vertical shift straight off a sine or cosine equation, then sketch the wave without plotting points.
Common Trigonometric Identities You Should Know
A reference to the Pythagorean, reciprocal, quotient, even-odd, and angle-sum identities, closing with a full exact verification of sin 75 degrees.
Solving a Right Triangle From Any Two Given Values
Every solvable right triangle starts from one of four input patterns — angle-and-hypotenuse, angle-and-leg, two legs, or leg-and-hypotenuse. Four fresh worked examples cover all four.
The Law of Sines and the Ambiguous SSA Case
Two sides and a non-included angle can describe two triangles, one, or none. A geometric height test and three worked examples — no solution, one, and two — settle every case.
The Law of Cosines: Derivation and When to Prefer It
A full geometric derivation of the Law of Cosines from the Pythagorean theorem, plus SAS and SSS worked examples showing exactly why it never runs into the ambiguity SSA does.
Degrees, Radians, and Gradians: Comparing Angle Units
Three ways to measure the same angle, compared side by side with a full conversion table and worked examples — and why only one of them is built from the circle's own geometry.
Inverse Trig Domains and Ranges: Why arcsin(sin x) Isn't Always x
arcsin, arccos, and arctan each return values from a restricted range, never the full circle. Real examples show what that restriction means, and where it trips people up.