Unit Circle Quiz

How to play

1. Start the quiz and read the entire question.
2. Choose one answer from the four options.
3. Read the feedback before moving to the next question.
4. Review your score and answers, then replay or retry the questions you missed.

Explore Unit Circle

Connect standard angles with coordinates, sine and cosine on the unit circle. This round uses exact values and conventional counterclockwise angles measured from the positive horizontal axis. A useful practice round connects each answer with a reason, not just a familiar-looking option.

At angle zero, the unit-circle point is (1, 0). At π/2, the unit-circle point is (0, 1). At π radians, the horizontal coordinate is −1. At 3π/2, the vertical coordinate is −1. A half-turn is 180° or π radians. The sine of π/6, or 30°, is 1/2. The cosine of π/3, or 60°, is 1/2. At π/4, sine and cosine are equal and nonzero, so tangent is 1. A unit-circle point has coordinates (cos θ, sin θ). A unit circle has radius one by definition.

When an answer surprises you, pause and explain the difference between the correct choice and your first guess. A replay changes the order of the choices, so remembering an option’s position is less useful than understanding the idea. Keep a short list of unfamiliar concepts and explore them with a reliable topic reference. The result is a score for this small question set, not a comprehensive assessment of your knowledge or a formal qualification.

Further reading:

Continue practising with IQ Quiz or change the challenge with Chemistry Quiz.

Frequently asked questions

Which unit-circle coordinate is sine?

Sine is the vertical y coordinate of the point at the stated angle.

Are degrees and radians the same numerical unit?

No. A full turn is 360° or 2π radians.

Why are exact values used instead of rounded decimals?

Exact values preserve the mathematical relationship and avoid rounding differences.

Is tangent defined wherever cosine is zero?

No. Tangent is sine divided by cosine and is undefined when cosine is zero.

Which way do positive angles run by convention?

They are measured counterclockwise from the positive horizontal axis in this activity.