ilearn.sfsu.edu C N Netflix i https:/ilearn.sfsu.edu/ay2122/pluginfile.php/884619/mod_resource/content/3/Exam 4. Nora is certain that cos(x + 12) = sinx. She is mistaken. Note: The unit circle could be very helpful in thinking about why Nora is mistaken and about the next questions. The graphs could also be very helpful. a. Show clearly that she is mistaken.* b. Now use another method to show her why she is mistaken. c. Write an equation that relates the sin and cosine functions that is correct. I d. Explain how you can check that your equation is correct. *Remember: you can show something is not always true by giving a counterexample. MacBook Air BEE F4 F5 457 DI F8 FO @ 3 A 8 Dilearn.sfsu.edu C N Netflix i https:/ilearn.sfsu.edu/ay2122/pluginfile.php/884619/mod_resource/content/3/Exam%203. 1. Choose your own numbers (other than 1 or 0) for the parameters: a, b, c, and d in y = asin(bx + c) + d a. Use Desmos to draw your graph and show a carefully drawn and scaled part of the graph for at least one full period. Explain its relation to the graph of y = sinx Note: Once you put your graph is Desmos you might find out that you don't like the numbers you chose. Remember you can change them and make adjustments so you can work with numbers and a graph you like better. Each person should have a different solution! b. For each parameter, give a new possible value to get your graph to: Shift up Shift to the left . . Stretch vertically Stretch out horizontally MacBook Air 8BE F4 F5 F6 DI F8 F9 AX FF @ 3 A & 8W ilearn.sfsu.edu C N Netflix https://ilearn.sfsu.edu/ay2122/pluginfile.php/884619/mod_resource/content/3/Exam 2. Let f(x) = tan(x)and g(x) = x -2. a. Determine the equation for f(g(x)) and use desmos to help you sketch its graph. Describe how this graph differs from the graph of tan(x). b. Determine the equation for g(f(x)) and draw its graph. Describe how this graph differs from the graph of tan(x). Self-assessment: How did you do on problem 2? Checks: Comments about your work: 3. Let f(x) = sinx and g(x) = cosx. Borley believes that fog(0) = gof (0). Is Borley correct? Show mathematically or explain why or why not. Self-assessment: How did you do on problem 3? Checks: Comments about your work: MacBook Air :9:F2 188: F4 F5 F6 DI F8 FI @ 3 OO 2 8