Core 4 Finding minimum value of trig equation Watch

koolgurl14
Badges: 9
Rep:
?
#1
Report Thread starter 2 years ago
#1
I know how to get max value but not min value q b i and ii
R = SQUARE ROOT 10
a is 1.25
Name:  tsr.png
Views: 101
Size:  119.9 KB
0
reply
Zacken
Badges: 22
Rep:
?
#2
Report 2 years ago
#2
(Original post by koolgurl14)
I know how to get max value but not min value q b i and ii
R = SQUARE ROOT 10
a is 1.25
The minimum value of \sin(x-\alpha) is -1, so the minimum value of R\sin(x-\alpha) = -R and this occurs precisely when \sin (x-\alpha) = -1 \Rightarrow x - \alpha = \frac{3\pi}{2} or some other reasonable value.
1
reply
Luke Kostanjsek
Badges: 10
Rep:
?
#3
Report 2 years ago
#3
Easiest way to do this is to say what value of sin(.....) makes sqrt10 sin(.....) as small as possible. Given as you know that sin(...) ranges from -1 to 1, the smallest value occurs when sin(......) is -1, so the minimum value is -sqrt10. As for the second part, you know that sin(x-1.25)=-1, so just solve for x.
1
reply
koolgurl14
Badges: 9
Rep:
?
#4
Report Thread starter 2 years ago
#4
(Original post by Zacken)
The minimum value of \sin(x-\alpha) is -1, so the minimum value of R\sin(x-\alpha) = -R and this occurs precisely when \sin (x-\alpha) = -1 \Rightarrow x - \alpha = \frac{3\pi}{2} or some other reasonable value.
Hmm what about R>0 or does that not affect the results
its the right answer btw im just asking why we should ignore the R>0
0
reply
Zacken
Badges: 22
Rep:
?
#5
Report 2 years ago
#5
(Original post by koolgurl14)
Hmm what about R>0 or does that not affect the results
its the right answer btw im just asking why we should ignore the R>0
What do you mean by ignoring R>0?

We have an expression R\sin(x-\alpha). To minimise this, we look at the variable terms and notice that \sin is bounded between -1 (minimum) and 1 (maximum), so to maximise our entire function we pick the minimum sine value and hence say that the minimum of R\sin(x-\alpha) = R(-1) = -R.
0
reply
KaylaB
Badges: 20
Rep:
?
#6
Report 2 years ago
#6
(Original post by koolgurl14)
Hmm what about R>0 or does that not affect the results
its the right answer btw im just asking why we should ignore the R>0
R>0 only applies to finding the value of R
1
reply
koolgurl14
Badges: 9
Rep:
?
#7
Report Thread starter 2 years ago
#7
Ahhh I see what you mean its just cause in the question it says the range of R is R>0 so I got confused but I guess its not actual R being less than 0?
0
reply
Zacken
Badges: 22
Rep:
?
#8
Report 2 years ago
#8
(Original post by koolgurl14)
Ahhh I see what you mean its just cause in the question it says the range of R is R>0 so I got confused but I guess its not actual R being less than 0?
Ohh, it just means that when you do R^2 = 1^2 + (-3)^2 = 10 then you have R = \pm \sqrt{10} but since R > 0 you pick R = \sqrt{10} since -\sqrt{10} < 0
0
reply
koolgurl14
Badges: 9
Rep:
?
#9
Report Thread starter 2 years ago
#9
(Original post by Zacken)
Ohh, it just means that when you do R^2 = 1^2 + (-3)^2 = 10 then you have R = \pm \sqrt{10} but since R > 0 you pick R = \sqrt{10} since -\sqrt{10} < 0

ohhhhhh that makes a lot of sense thanks alot
0
reply
Zacken
Badges: 22
Rep:
?
#10
Report 2 years ago
#10
(Original post by koolgurl14)
ohhhhhh that makes a lot of sense thanks alot
No problem!
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of Derby
    Postgraduate and Professional Open Evening - Derby Campus Postgraduate
    Tue, 22 Jan '19
  • University of the West of England, Bristol
    Undergraduate Open Afternoon - Frenchay Campus Undergraduate
    Wed, 23 Jan '19
  • University of East London
    Postgraduate Open Evening Postgraduate
    Wed, 23 Jan '19

Brexit: Given the chance now, would you vote leave or remain?

Remain (1526)
79.27%
Leave (399)
20.73%

Watched Threads

View All