📐Unit Circle Trigonometry · Sec 3–4
🖱️Drag the point on the circle or use the slider
🧠Watch how sin θ and cos θ move together
How to use this interactive
- Drag the blue point on the unit circle or use the angle slider.
- Switch between degrees and radians to see how the same angle is written in both units.
- Watch the triangle, exact values, and sine/cosine graphs update in real time.
- Use the practice question box to generate random angles and reveal step-by-step working with hints and “Why?” explanations.
- Try typing your own expression in the equation box – the on-screen math keyboard can help.
The log at the bottom records each action, so teachers can replay what you explored.
Angle controls
Move the angle, then read the values of sin θ and cos θ.
θ:45°
Q I
sin θ
0.7071
= \(\tfrac{\sqrt{2}}{2}\)
cos θ
0.7071
= \(\tfrac{\sqrt{2}}{2}\)
Unit circle
Drag the blue point around the circle.
Horizontal projection = cos θ, vertical projection = sin θ.
Triangle (SOH-CAH-TOA)
Right triangle linked to the circle.
Opp:0.71
Adj:0.71
Hyp:1.00
Graphs of y = sin x and y = cos x
Angle θ is marked on both graphs.
Practice & step-by-step solutions
Generate an angle and work through the reasoning.
Special angles on the unit circle are used for practice.
Click “New random angle” to start.
LaTeX-style preview will appear here.
Interaction log
Timeline of your actions (for teachers).