Unit Circle Worksheet

Goal: Read sine, cosine and tangent from the unit circle, connect degrees to radians, and use symmetry to predict values in every quadrant.

Tool: Unit circle at geometrylab.net/unit-circle/ · Connects to Common Core HSF-TF.A.2

What to do

1. Open the unit circle. Type 30 into “Angle θ” (or press the “30°” button) and record the radians, cos θ, sin θ and tan θ.
2. Repeat for every angle in the table. Type angles that have no button, such as 150, straight into “Angle θ”.
3. Drag the point slowly all the way around the circle. Watch how the signs of cos θ and sin θ change from quadrant to quadrant.

Record your results

Questions

1. At 60°, the point on the circle is (cos θ, sin θ) = (½, √3/2). Show that sin²θ + cos²θ = 1 for this angle.

2. Why is tan 90° undefined?

3. Compare 30° and 150°. Which values are equal, which are opposite, and why?

4. In which quadrant are both cos θ and sin θ negative? Give an angle from your table that shows it.

5. Convert 225° to radians by hand, then check your table.

6. Predict sin 330° and cos 330° without the tool, then check.

Free from Geometry Lab · geometrylab.net · HSF-TF.A.2: Explain how the unit circle extends trigonometric functions to all real numbers, interpreted as radian measures of angles.

Teaching with this? Find the answer key and more activities on the Geometry Lab for teachers page.