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

Remindersy = sinx y = cosx

Max at x = 900

Min at x = 2700

Max at x = 00

and 3600

Min at x = 1800

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

-57

-7

5!!!!!

So Max Value of

6Cosx + 7

This occurs when x = 00 or 3600

= 6 + 7

= 13

Careful

So Max Value of

5 – 7sinx

= 5 + 7

= 12

So Max Value of

7Sinx - 3

This occurs when x = 900

= 7 - 3

= 4

Nastier

Max value of

5sin(x – 20)0

Max value = 5 Occurs when……

Reminder:

5sinx has max when x = 900

so 5sin(x - 20)0 has max when x – 20 = 90

x = 110

Want this to equal 900

Nastier (but we’re getting the hang of it!)

Max value of

9sin(x + 30)0

Max value = 9

9sinx has max when x = 900

so 9sin(x + 30)0 has max when x + 30 = 90

x = 60

Want this to equal 900

Nastier (almost there!)Max value of

11cos(x - 70)0

Max value = 11 Reminder:

11cosx has max when x = 00 or 3600

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 = 430Outwith limits

Want this to equal 00 or 3600

Max and Min Trig Valuesy = sinx y = cosx

Max at x = 900

Min at x = 2700

Max at x = 00

and 3600

Min at x = 1800

So Max Value of

9Cosx + 4

This occurs when x = 00 or 3600

= 9 + 4

= 13

Nastier

Max value of

4sin(x - 30)0

Max value = 4

4sinx has max when x = 900

so 4sin(x - 30)0 has max when x - 30 = 90

x = 120

Want this to equal 900

Nastier (last one!)Max value of

3sin(x – π/4)

Max value = 3

Max value of 3sinx occurs when x = 900

= π/2

3sin(x – π/4) has max when

x - π/4 = π/2

x = π/2 + π/4

= 3π/4

Even NastierMax value of

6sin(x + π/4)

Max value = 6

Max value of 6sinx occurs when x = 900

= π/2

6sin(x + π/4) has max when

x + π/4 = π/2

x = π/2 - π/4

= π/4