Max and Min Trig Values. What is to be learned How to find the maximum and minimum values of trig...
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Transcript of Max and Min Trig Values. What is to be learned How to find the maximum and minimum values of trig...
![Page 1: 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.](https://reader035.fdocuments.us/reader035/viewer/2022081821/56649f495503460f94c6b859/html5/thumbnails/1.jpg)
Max and Min Trig Values
![Page 2: 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.](https://reader035.fdocuments.us/reader035/viewer/2022081821/56649f495503460f94c6b859/html5/thumbnails/2.jpg)
What is to be learned
• How to find the maximum and minimum values of trig functions.
• How to find when they occur
![Page 3: 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.](https://reader035.fdocuments.us/reader035/viewer/2022081821/56649f495503460f94c6b859/html5/thumbnails/3.jpg)
Remindersy = sinx y = cosx
Max at x = 900
Min at x = 2700
Max at x = 00
and 3600
Min at x = 1800
![Page 4: 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.](https://reader035.fdocuments.us/reader035/viewer/2022081821/56649f495503460f94c6b859/html5/thumbnails/4.jpg)
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!!!!!
![Page 5: 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.](https://reader035.fdocuments.us/reader035/viewer/2022081821/56649f495503460f94c6b859/html5/thumbnails/5.jpg)
So Max Value of
6Cosx + 7
This occurs when x = 00 or 3600
= 6 + 7
= 13
![Page 6: 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.](https://reader035.fdocuments.us/reader035/viewer/2022081821/56649f495503460f94c6b859/html5/thumbnails/6.jpg)
Careful
So Max Value of
5 – 7sinx
= 5 + 7
= 12
![Page 7: 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.](https://reader035.fdocuments.us/reader035/viewer/2022081821/56649f495503460f94c6b859/html5/thumbnails/7.jpg)
So Max Value of
7Sinx - 3
This occurs when x = 900
= 7 - 3
= 4
![Page 8: 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.](https://reader035.fdocuments.us/reader035/viewer/2022081821/56649f495503460f94c6b859/html5/thumbnails/8.jpg)
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
![Page 9: 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.](https://reader035.fdocuments.us/reader035/viewer/2022081821/56649f495503460f94c6b859/html5/thumbnails/9.jpg)
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
![Page 10: 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.](https://reader035.fdocuments.us/reader035/viewer/2022081821/56649f495503460f94c6b859/html5/thumbnails/10.jpg)
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
![Page 11: 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.](https://reader035.fdocuments.us/reader035/viewer/2022081821/56649f495503460f94c6b859/html5/thumbnails/11.jpg)
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
![Page 12: 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.](https://reader035.fdocuments.us/reader035/viewer/2022081821/56649f495503460f94c6b859/html5/thumbnails/12.jpg)
So Max Value of
9Cosx + 4
This occurs when x = 00 or 3600
= 9 + 4
= 13
![Page 13: 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.](https://reader035.fdocuments.us/reader035/viewer/2022081821/56649f495503460f94c6b859/html5/thumbnails/13.jpg)
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
![Page 14: 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.](https://reader035.fdocuments.us/reader035/viewer/2022081821/56649f495503460f94c6b859/html5/thumbnails/14.jpg)
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
![Page 15: 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.](https://reader035.fdocuments.us/reader035/viewer/2022081821/56649f495503460f94c6b859/html5/thumbnails/15.jpg)
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