Max and Min Trig Values

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

Reminders y = sinxy = cosx Max at x = 90 0 Min at x = Max at x = 0 0 and Min at x = 180 0

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 !!!!!

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

Careful So Max Value of 5 – 7sinx = = 12

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

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

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

Nastier (almost there!) Max value of 11cos(x - 70) 0 Max value = 11 Reminder: 11cosx has max when x = 0 0 or 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

Max and Min Trig Values y = sinxy = cosx Max at x = 90 0 Min at x = Max at x = 0 0 and Min at x = 180 0

So Max Value of 9Cosx + 4 This occurs when x = 0 0 or = = 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

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

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