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C2 urgent trig question help
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Butterflyshy
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#1
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.
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_gcx
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#2
(Original post by Butterflyshy)
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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.
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.
and 
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?
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Butterflyshy
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#3
(Original post by _gcx)
The minimum value of both and 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?
The minimum value of both
and 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?
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_gcx
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#4
(Original post by Butterflyshy)
Sorry to bother but can you help me go through part b.
Sorry to bother but can you help me go through part b.
is -1. How can we use this to get a minimum value of y? (try substituting)
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Butterflyshy
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#5
(Original post by _gcx)
The minimum value of is -1. How can we use this to get a minimum value of y? (try substituting)
The minimum value of
is -1. How can we use this to get a minimum value of y? (try substituting)
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Zacken
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#6
(Original post by Butterflyshy)
how did you get sin(3x-45)
how did you get sin(3x-45)
where 
. 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...
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Butterflyshy
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#7
(Original post by Zacken)
He confused (c) and (b). Anyway for (b), you have something of the form where . 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...
He confused (c) and (b). Anyway for (b), you have something of the form
where . 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
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Zacken
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Butterflyshy
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#9
(Original post by Zacken)
No problem.
No problem.
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Zacken
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#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?
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?
Like wise for min and sin(x+30) = -1
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Butterflyshy
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#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
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
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Zacken
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