This worksheet is intended for students to make connections between the unit circle and the trigonometric functions. You can manipulate the point on the unit circle and see how it corresponds to the 3 basic trigonometric functions.
Part 1. Select the sin(x) check box and you will see the sine curve displayed on the graph. Move point C and answer the following questions: 1) Examining the x-values. a. What does the x-axis represent? b. How is it connected to the unit circle? 2) Examining the y-values. a. What does the y-axis represent? b. How is it connected to the unit circle? 3) Explain why manipulating point c only corresponds to the graph from 0 – 2π. 4) Now move point B. How does point B affect the graph? Why? Part 2. Select the cos(x) check box and you will see the sine curve displayed on the graph. Move point C and answer the following questions: 1) Examining the x-values. a. What does the x-axis represent? b. How is it connected to the unit circle? 2) Examining the y-values. a. What does the y-axis represent? b. How is it connected to the unit circle? 3) Explain why manipulating point c only corresponds to the graph from 0 – 2π. 4) Now move point B. How does point B affect the graph? Part 3. Select the tan(x) check box and you will see the sine curve displayed on the graph. Move point C and answer the following questions: 1) Examining the x-values. a. What does the x-axis represent? b. How is it connected to the unit circle? 2) Examining the y-values. a. What does the y-axis represent? b. How is it connected to the unit circle? 3) Explain why manipulating point c only corresponds to the graph from 0 – 2π. 4) Now move point B. How does point B affect the graph? 5) How is the graph of tan(x) different then the graphs of cos(x) and sin(x)? (refer to the unit circle)