C2 urgent trig question help

Watch this thread
Butterflyshy
Badges: 12
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#1
Report Thread starter 5 years ago
#1
Name:  WhatsApp Image 2017-03-23 at 20.52.23.jpeg
Views: 138
Size:  104.7 KB

I need help with question 11. For part (a) I managed to answer it by trial and error. I need someone to explain how to do these questions. One thing I do know is the that the values of cos and sin are between -1 and 1.
0
reply
_gcx
Badges: 21
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#2
Report 5 years ago
#2
(Original post by Butterflyshy)
Name:  WhatsApp Image 2017-03-23 at 20.52.23.jpeg
Views: 138
Size:  104.7 KB

I need help with question 11. For part (a) I managed to answer it by trial and error. I need someone to explain how to do these questions. One thing I do know is the that the values of cos and sin are between -1 and 1.
The minimum value of both sin(x) and cos(x) is -1, similarly the maximum value of both is 1. How can we use that information to determine a minimum and maximum value of y, and hence the values for x for which this value of y occurs?
0
reply
Butterflyshy
Badges: 12
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#3
Report Thread starter 5 years ago
#3
(Original post by _gcx)
The minimum value of both sin(x) and cos(x) is -1, similarly the maximum value of both is 1. How can we use that information to determine a minimum and maximum value of y, and hence the values for x for which this value of y occurs?
Sorry to bother but can you help me go through part b.
0
reply
_gcx
Badges: 21
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#4
Report 5 years ago
#4
(Original post by Butterflyshy)
Sorry to bother but can you help me go through part b.
The minimum value of sin(3x-45) is -1. How can we use this to get a minimum value of y? (try substituting)
0
reply
Butterflyshy
Badges: 12
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#5
Report Thread starter 5 years ago
#5
(Original post by _gcx)
The minimum value of sin(3x-45) is -1. How can we use this to get a minimum value of y? (try substituting)
how did you get sin(3x-45)
0
reply
Zacken
Badges: 22
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#6
Report 5 years ago
#6
(Original post by Butterflyshy)
how did you get sin(3x-45)
He confused (c) and (b). Anyway for (b), you have something of the form y = 5 - 4a where a = \sin(x+ 30). Now you want to make y as big as possible. Since y is of the form 5 - 4a, you want to then make 4a as small as possible since then you're subtracting the smallest number possible from 5, hence giving you the biggest y possible.

Now to make 4a as small as possible, you simply need to see how small a can get, then multiply that value by 4 to see how small 4a can get.

Since a = sin(x+30), which at it's very smallest is -1. Then 4a at it's very smallest is -4.

So y = 5 - 4a is at it's biggest when y = 5-(-4) = 9. That's the maximum.

Similarly to make y as small as possible, we want to make a as big as possible so that you're subtracting the biggest number possible from 5 to get the smallest y possible. Blah blah blah...

can you see the general techniques here, all it relies on is the fact that sin and cos are bounded between -1 and 1 and then using common sense to find the maximum and minimum of functions involving sines and cosines.

Let me know if this needs more clearing up...
2
reply
Butterflyshy
Badges: 12
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#7
Report Thread starter 5 years ago
#7
(Original post by Zacken)
He confused (c) and (b). Anyway for (b), you have something of the form y = 5 - 4a where a = \sin(x+ 30). Now you want to make y as big as possible. Since y is of the form 5 - 4a, you want to then make 4a as small as possible since then you're subtracting the smallest number possible from 5, hence giving you the biggest y possible.

Now to make 4a as small as possible, you simply need to see how small a can get, then multiply that value by 4 to see how small 4a can get.

Since a = sin(x+30), which at it's very smallest is -1. Then 4a at it's very smallest is -4.

So y = 5 - 4a is at it's biggest when y = 5-(-4) = 9. That's the maximum.

Similarly to make y as small as possible, we want to make a as big as possible so that you're subtracting the biggest number possible from 5 to get the smallest y possible. Blah blah blah...

can you see the general techniques here, all it relies on is the fact that sin and cos are bounded between -1 and 1 and then using common sense to find the maximum and minimum of functions involving sines and cosines.

Let me know if this needs more clearing up...

Thanks so much
0
reply
Zacken
Badges: 22
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#8
Report 5 years ago
#8
(Original post by Butterflyshy)
Thanks so much
No problem.
0
reply
Butterflyshy
Badges: 12
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#9
Report Thread starter 5 years ago
#9
(Original post by Zacken)
No problem.
I now understand where the values of y occur but how would find the values of x. For example the max and min for part a are 2 and 0 and they occur at 90 degrees and 180 degrees?
0
reply
Zacken
Badges: 22
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#10
Report 5 years ago
#10
(Original post by Butterflyshy)
I now understand where the values of y occur but how would find the values of x. For example the max and min for part a are 2 and 0 and they occur at 90 degrees and 180 degrees?
Well to find the max of y, you had to set sin (x+30) = 1. Now you solve this equation for x.

Like wise for min and sin(x+30) = -1
0
reply
Butterflyshy
Badges: 12
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#11
Report Thread starter 5 years ago
#11
(Original post by Zacken)
Well to find the max of y, you had to set sin (x+30) = 1. Now you solve this equation for x.

Like wise for min and sin(x+30) = -1
Thanks I'm getting the right answer.
0
reply
Zacken
Badges: 22
Rep:
? You'll earn badges for being active around the site. Rep gems come when your posts are rated by other community members.
#12
Report 5 years ago
#12
(Original post by Butterflyshy)
Thanks I'm getting the right answer.
Great.
0
reply
X

Quick Reply

Attached files
Write a reply...
Reply
new posts
Back
to top
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

How did your AQA A-level Psychology Paper 1 go?

Loved the paper - Feeling positive (48)
49.48%
The paper was reasonable (37)
38.14%
Not feeling great about that exam... (8)
8.25%
It was TERRIBLE (4)
4.12%

Watched Threads

View All