📐 Free Trigonometry Quiz

UNIT CIRCLE
QUIZ

Test your mastery of theunit circle— angles in degrees and radians, sine, cosine, and tangent values at key positions.

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Trigonometry

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What Is the Unit Circle?

Theunit circleis a circle of radius 1 centred at the origin of a coordinate plane. It is fundamental to trigonometry because it defines the sine and cosine functions for all angles, making complex calculations much simpler.

Key Angles to Know

The most important angles on the unit circle are0°, 30°, 45°, 60°, and 90°and their equivalents in other quadrants. Memorising their radian values (0, π/6, π/4, π/3, π/2) is essential for success in pre-calculus and calculus courses.

Sine, Cosine, and Tangent

For any angle θ on the unit circle, the x-coordinate iscos(θ)and the y-coordinate issin(θ). Tangent is defined as sin(θ)/cos(θ).

Memory Tricks

Use the mnemonicSOHCAHTOA— Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent.
For 30-60-90 triangles: sides are in ratio1 : √3 : 2.
For 45-45-90 triangles: sides are in ratio1 : 1 : √2.

Unit Circle Quiz — FAQ

What does the unit circle quiz test?

This quiz covers radian and degree conversions, sine and cosine values at standard angles, tangent values, and quadrant identification.

Do I need to memorise the unit circle?

Yes — for most standardised tests and calculus courses, you are expected to recall key values (sin 30° = 0.5, cos 60° = 0.5, etc.) from memory without a calculator.

What is π/6 in degrees?

π/6 radians equals30 degrees. The conversion formula is: degrees = radians × (180/π).

What is the value of sin(90°)?

sin(90°) =1. At 90° (π/2 radians) on the unit circle, the coordinate is (0, 1), so the y-value (sine) is 1.