Min and Max Trig Values

1. Block 3
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 = sinx y = cosx
Max at x = 900
Min at x = 2700
Max at x = 00
and 3600
Min at x = 1800

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
-5

5. So Max Value of
6Cosx + 7
This occurs when x = 00
or 3600
= 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 = 900
= 7 – 3
= 4

8. 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

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 = 900
so 9sin(x + 30)0
has max when x + 30 = 90
x = 60
Want this to
equal 900

10. 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 = 430
Outwith limits
Want this to
equal 00
or
3600

11. Max and Min Trig Values
y = sinx y = cosx
Max at x = 900
Min at x = 2700
Max at x = 00
and 3600
Min at x = 1800

12. So Max Value of
9Cosx + 4
This occurs when x = 00
or 3600
= 9 + 4
= 13

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

14. 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
Want this to
equal π
/2
radians

15. Even Nastier
Max 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 radians
Want this to
equal π
/2

16. Key QuestionMax value of y = 2 cos (x + π
/4)
and corresponding value of x.
Max value = 2
Max value of 2cosx occurs when x = 00
or 3600
= 0 rads or 2π rads
2cos(x + π
/4)has max when
x + π
/4 = 0
x = - π
/4 (outwith limits)
OR x + π
/4 = 2π
x = 2π – π
/4
7π
radians