Relating the Unit Circle to the trigonometric curves
- Donald C. Albin Jr.
Submitted by Mr. Donald C. Albin Jr. Professional Educator www.donaldalbin.99k.org Explore the relationship between the unit circle and the trigonometric curves for sine and cosine. Directions
- Move the blue circle around the unit circle. Observe how the two points move along the sine and cosine curves.
Questions to promote inquiry
- How can you read the value of the sine function from the unit circle?
- How can you read the value of the cosine function from the unit circle?
- Compare and contrast the axes of the unit circle and the trigonometric curves.
- The tangent is not shown. Name three ways of identifying the tangent from the graphs.
- What happens to the trigonometric curves when θ is less than zero or greater than 2π?
- The amplitude and period are shown on the graph of the trigonometric curves. Note that the period is measured 'peak-to-peak'. Period and amplitude have physical meaning in the unit circle also. What is the physical meaning of amplitude and period in the unit circle?