Trig Drills
sin, cos, tan - pick the right value for any reference angle. Drills from 0° to 360° across all four quadrants
About Trig Drills
Trig Drills trains your recall of sine, cosine, and tangent values for the 16 reference angles · the same angles every trig textbook puts on the unit circle. Each round names a function and an angle (sin 30°, cos 120°, tan 225°) and you pick the correct exact value from four choices. The point is to make the reference values automatic, the way times tables become automatic with practice.
Exact symbolic values, not decimals. Answers are always exact fractions or radicals · 1/2, √3/2, √3/3, −√2/2 · never decimal approximations. Real trig fluency means knowing sin(60°) = √3/2, not 0.866. The exact-value form is what you actually use in calculus integrals, physics derivations, and engineering formulas; the decimal is a computed artefact.
The 16 reference angles. The full set: 0°, 30°, 45°, 60°, 90°, 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, 330°. Three families · multiples of 30° (which give halves and √3/2 values), multiples of 45° (which give √2/2 values), and the axis-crossings at 0° / 90° / 180° / 270°. Memorising the first quadrant (0° to 90°) plus the sign rules for the other three is the actual minimum, and the game is structured to teach exactly that.
Difficulty scales the angle range. Level 1-3 covers sin and cos only across the first quadrant (0-90°) · the foundational set. Level 4-6 adds tangent and extends to 180°. Level 7-10 covers all three functions across all four quadrants · so the player has to handle the signs (cos is negative in Q2 and Q3, sin is negative in Q3 and Q4, tan is positive in Q1 and Q3 only). High-level rounds also include tan at 90° and 270°, where the answer is "undefined" because cosine is zero.
Part of the PlayMemorize family of brain-training games. Runs entirely in your browser, works offline as a Progressive Web App.
FAQ
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What angles are covered?
The 16 reference angles: 0°, 30°, 45°, 60°, 90°, 120°, 135°, 150°, 180°, 210°, 225°, 240°, 270°, 300°, 315°, and 330°. Three families · multiples of 30°, multiples of 45°, and the four axis-crossings. -
Why exact fractions instead of decimals?
Real trig fluency means knowing sin(30°) = 1/2, not 0.5. Exact values are what you actually use in calculus integrals, physics formulas, and engineering derivations · the decimal form is a computed artefact, not the answer. Memorising the exact values is what makes downstream maths possible without a calculator. -
What happens at 90° and 270° for tangent?
Tangent is undefined at those angles because tan = sin/cos and cos(90°) = cos(270°) = 0 · division by zero. The game shows "undefined" as an answer choice and that's the correct pick for those rounds. -
How does difficulty work?
Difficulty 1-2 drills sin and cos in quadrant I (0-90°) · the foundational set. Difficulty 3-6 adds tangent and extends to 180°. Difficulty 7-10 covers all three functions across all four quadrants, so you have to handle the sign rules (cos negative in Q2-Q3, sin negative in Q3-Q4) as well as the magnitudes.