1. Max and Min Trig Values

2. What is to be learned How to find the maximum and minimum values of trig functions. How to find when they occur

3. Reminders y = sinxy = cosx Max at x = 90 0 Min at x = 270 0 Max at x = 0 0 and 360 0 Min at x = 180 0

4. More Reminders Max value of 5sinx is Min value of 5sinx is Max value of 7cosx is Min value of 7Cos x is Max value of -5Cosx is 5 -5 7 -7 5!!!!!

5. So Max Value of 6Cosx + 7 This occurs when x = 0 0 or 360 0 = 6 + 7 = 13

6. Careful So Max Value of 5 – 7sinx = 5 + 7 = 12

7. So Max Value of 7Sinx - 3 This occurs when x = 90 0 = 7 - 3 = 4

8. Nastier Max value of 5sin(x – 20) 0 Max value = 5 Occurs when……  Reminder: 5sinx has max when x = 90 0 so 5sin(x - 20) 0 has max when x – 20 = 90 x = 110 Want this to equal 90 0

9. Nastier (but we’re getting the hang of it!) Max value of 9sin(x + 30) 0 Max value = 9 9sinx has max when x = 90 0 so 9sin(x + 30) 0 has max when x + 30 = 90 x = 60 Want this to equal 90 0

10. Nastier (almost there!) Max value of 11cos(x - 70) 0 Max value = 11 Reminder: 11cosx has max when x = 0 0 or 360 0 so 11cos(x - 70) 0 has max when x - 70 = 0 x = 70 or 11cos(x - 70) 0 has max when x - 70 = 360 x = 430 Outwith limits Want this to equal 0 0 or 360 0

11. Max and Min Trig Values y = sinxy = cosx Max at x = 90 0 Min at x = 270 0 Max at x = 0 0 and 360 0 Min at x = 180 0

12. So Max Value of 9Cosx + 4 This occurs when x = 0 0 or 360 0 = 9 + 4 = 13

13. Nastier Max value of 4sin(x - 30) 0 Max value = 4 4sinx has max when x = 90 0 so 4sin(x - 30) 0 has max when x - 30 = 90 x = 120 Want this to equal 90 0

14. Nastier (last one!) Max value of 3sin(x – π / 4 ) Max value = 3 Max value of 3sinx occurs when x = 90 0 = π / 2 3sin(x – π / 4 ) has max when x - π / 4 = π / 2 x = π / 2 + π / 4 = 3π / 4

15. Even Nastier Max value of 6sin(x + π / 4 ) Max value = 6 Max value of 6sinx occurs when x = 90 0 = π / 2 6sin(x + π / 4 ) has max when x + π / 4 = π / 2 x = π / 2 - π / 4 = π / 4