Unit Circle Lab
Radians, exact values and trig graphs, all drawn on the unit circle.
Unit Circle Lab makes the unit circle something students can see and use. The game starts with converting between degrees and radians, then moves to reference angles and to the coordinates of points on the circle. The circle is drawn from real coordinates, with negative angles swept clockwise and extra turns past 360 degrees.
Next come exact values of sine, cosine and tangent at the standard angles, the signs in each quadrant and coterminal angles. Students then read the amplitude, period and midline of a sine or cosine equation, and finish with inverse trig values and the double angle identities. Every answer is exact, so no calculator rounding is needed.
What children practice
- Convert between degrees and radians in both directions
- Find the reference angle for an angle in any quadrant
- Read the coordinates of a point on the unit circle as cosine and sine
- Write exact sine, cosine and tangent values at the standard angles
- Use quadrant signs and find coterminal angles
- Read amplitude, period and midline, and use inverse trig and double angle identities
Levels
- Degrees and radians: Convert both ways
- Reference angles: The acute angle to the x axis
- Angles and points: Coordinates on the circle
- Exact values: Sine, cosine, tangent
- Signs and full turns: Quadrants, coterminal angles
- Sine and cosine graphs: Amplitude, period, midline
- Inverse trig, identities: Principal values, double angles
- Course mix: Everything on the circle
How it works
- Eight levels go from degrees and radians to inverse trig and identities, and the last level mixes the whole circle.
- Tangent at 90 and 270 degrees is shown as not defined, and exact values put any radical on top.
- Five correct answers plus the practice timer open the next level, one step at a time.
- Answers come from choices, typed numbers, tapping parts of the drawing, matching and sorting.
Best for: A good fit for grades 10 to 12 in Algebra 2 or Precalculus when students are moving from triangle trig to the circle and need exact values to feel natural.
Tip for parents: Draw a circle and mark 30, 45 and 60 degrees in the first quarter. Ask your child to say each angle in radians, then see how many of the other quadrants they can fill in by symmetry.
Questions parents ask
Does the game expect students to memorize the whole circle?
It encourages seeing patterns instead. Reference angles and quadrant signs let students get from the first quadrant to every other one.
How are radical answers written?
Values such as root 3 over 2 are written with the radical on top and no radical in the denominator, so one third root 3 appears as root 3 over 3. Each answer has one written form.
Does it cover graphs of sine and cosine?
Level 6 does. Students read the amplitude, period and midline from an equation such as y equals 3 sin 2x plus 1, and the graph is drawn from the same equation.
Ready to try it?
Unit Circle Lab is free with a parent account. A parent adds a child profile, and the child's progress is saved.