PreCalculus Assignment 21 Graphing Tangent and Cotangent Writing answers on the worksheet is OK. 1. The tangent ratio is the slope of the line OT. It is also the length of the line AT. Show below why this is true using similar triangles. 2. Graph the tangent function below. 3. What is the period of the tangent function? 4. Write an equation that describes the values of 𝜃 for all real zeros. 5. What is the slope of the line OT on the unit circle when there is a zero of the function? 6. Write an equation that describes the values of 𝜃 for all the asymptotes. 7. What is the slope of the line OT on the unit circle when there is an asymptote on the graph? Why does this happen? 8. What is the domain and range of the function 𝑓 𝑥 = tan 𝑥. Explain how you know. ! 9. We know that cot 𝜃 = !. It is also equal to the length of line AC. Show why this is true using similar triangles. 10. Graph the cotangent function. 11. What is the period of the cotangent function? 12. Complete the table below to describe the features of the cotangent function. Location of all real zeros Location of all asymptotes On the function’s graph. On the unit circle. 13. What is the domain and range of the function 𝑓 𝑥 = cot 𝑥. Explain how you know. 14. What transformations of the function graph of 𝑦 = tan 𝜃 will result in the function graph of 𝑦 = cot 𝜃? 15. Use the values given to complete the table. 16. 17. Given is the graph of 𝑦 = sec 𝑡. a. Describe the location of all the asymptotes. b. Describe the domain and range of the function.