3. Use your unit circle and fill in the exact values of the cosine function for each of the following angles (measured in radians).
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1 Graphing Sine and Cosine Functions Desmos Activity 1. Use your unit circle and fill in the exact values of the sine function for each of the following angles (measured in radians). sin 0 sin π 2 sin π sin 3π 2 sin 2π 2. Use the values in the table above to graph one cycle of the sine curve on the coordinate plane below. 3. Use your unit circle and fill in the exact values of the cosine function for each of the following angles (measured in radians). cos 0 cos π 2 cos π cos 3π 2 cos 2π
2 4. Use the values in the table on the previous page to graph one cycle of the cosine curve on the coordinate plane below. 5. Use an ipad to visit the website student.desmos.com. Enter the class code written on the board. This differs by class period. Your code:. 6. Check your sine and cosine graphs with the graphs on slides 2 and 3 in the activity. 7. Go to slide 4. On this slide, you are going to work with the general form of the sine and cosine equations: y = A sin Bx C + D note: the functions sine and cosine are interchangeable in the equation. 8. Use the sliders in the activity to change the value of A. Then answer the following questions (hint, use the word vertical to describe what is happening): o What happens to the graph when A > 1? o What happens to the graph when A < 1 but is still positive? o What happens to the graph when you allow A to be negative? Be specific.
3 9. Use the sliders in the activity to change the value of B. The time it takes for the graph to complete one cycle is called the function s period. Make sure when you answer the two questions below, you talk about what happens horizontally to the graph and how the period is changed. Hint, the period is 2π B for sine and cosine functions. o What happens when B > 1? o What happens when B < 1 but is still positive? 10. Use the sliders in the activity to change the value of C. o What happens when you make C positive? o What happens when you make C negative? 11. Use the sliders in the activity to change the value of D. o What happens when you make D positive? o What happens when you make D negative? 12. Is everything the same when we graph cosine? If we change A, B, C and D, do the changes affect this graph the same way they did the sine curve?
4 13. Answer the question on slide 6. MULTIPLE CHOICE: Choose the definition below that best describes what is changed in the graph by changing the value of A in the equation f x = A sin Bx C + D. 14. What is the formula for amplitude? (slide 7) 15. What is the amplitude of the graph on slide 8? 16. MULTIPLE CHOICE: Choose the definition below that best describes what is changed in the graph by changing the value of B in the equation f x = A cos Bx C + D. 17. What is the formula for period (slide 10)? 18. What is the period of the blue graph on slide 11?
5 19. MULTIPLE CHOICE: Choose the definition below that best describes what is changed in the graph by changing the value of C in the equation f x = A sin Bx C + D. 20. What is the formula for phase shift (slide 13)? 21. What is the phase shift of the blue graph on slide 14? 22. MULTIPLE CHOICE: Choose the definition below that best describes what is changed in the graph by changing the value of D in the equation f x = A cos Bx C + D. 23. What is the formula for vertical shifts? (slide 16). 24. What is the vertical shift of the blue graph on slide 17? 25. Write an equation for the sine curve on slide 18.
6 Practice Problems: Graph each of the following functions. You can type the equation into a blank Desmos screen to check it. To do so, just open the Desmos app or go to instead of the student site. 1. y = 3 sin x 2. y = 2 cos x 3. y = cos(4x) 4. y = sin x 3 5. y = { sin x 6. y = ({ cos x)
7 7. y = cos(x π) 8. y = sin x + } 9. y = cos x ~} 10. y = sin ~ x
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