Alevel maths question

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Jessica_rica
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#1
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#1
Could someone please explain with modelling trigonometric functions how to to know when the minimum or maximum values are -1 or 1.
For instance with
P=11.5-0.5sin(t-2) the Max value is when sin(t-2)=-1 whic gives 12 in total, so the min value is when sin(t-2)= 11. I assumed that because it’s sin(t-2) which is the negative, we reflect the sin graph against the x-axis so the max value becomes -1.
But with another qs
P=17.4+2sin(0.7t-3) maximum value is when sin(0.7t-3)=1 which gives £19.40

Or does this depend on the context of the question given? if so how do you identify when to use the maximum or minimum as -1 or 1
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RDKGames
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#2
Report 2 years ago
#2
(Original post by Jessica_rica)
Could someone please explain with modelling trigonometric functions how to to know when the minimum or maximum values are -1 or 1.
For instance with
P=11.5-0.5sin(t-2) the Max value is when sin(t-2)=-1 whic gives 12 in total, so the min value is when sin(t-2)= 11. I assumed that because it’s sin(t-2) which is the negative, we reflect the sin graph against the x-axis so the max value becomes -1.
But with another qs
P=17.4+2sin(0.7t-3) maximum value is when sin(0.7t-3)=1 which gives £19.40

Or does this depend on the context of the question given? if so how do you identify when to use the maximum or minimum as -1 or 1
P = 11.5 - 0.5sin(t-2)

In this expression you have (constsnt) TAKE AWAY (a function)

and since its take away, it means that in order maximise P you want to take away as little as possible from the constant.

The smallest value sin can take is -1 hence why this corresponds to the max.


On the other hand, the other function has (constant) PLUS (a function) where in order to maximise you want to add on as much as possible hence the value of sin is 1.
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mnot
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#3
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#3
(Original post by Jessica_rica)
Could someone please explain with modelling trigonometric functions how to to know when the minimum or maximum values are -1 or 1.
For instance with
P=11.5-0.5sin(t-2) the Max value is when sin(t-2)=-1 whic gives 12 in total, so the min value is when sin(t-2)= 11. I assumed that because it’s sin(t-2) which is the negative, we reflect the sin graph against the x-axis so the max value becomes -1.
But with another qs
P=17.4+2sin(0.7t-3) maximum value is when sin(0.7t-3)=1 which gives £19.40

Or does this depend on the context of the question given? if so how do you identify when to use the maximum or minimum as -1 or 1
So the Max value of Sin or Cos function will be 1 (and minimum -1) ie where F(x) = Sin(G(x)) , F(x) maximum is 1, and G(x) is some value.

now for function P its a constant ( C ) + or - F(x) , after this point your literally doing addition or subtraction and it should be obvious which value is bigger and which is smaller... (this bit is not A-level maths, your teachers & exam boards will assume you can do the basic maths functions)
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GrayestOwl0900
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#4
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#4
(Original post by Jessica_rica)
Could someone please explain with modelling trigonometric functions how to to know when the minimum or maximum values are -1 or 1.
For instance with
P=11.5-0.5sin(t-2) the Max value is when sin(t-2)=-1 whic gives 12 in total, so the min value is when sin(t-2)= 11. I assumed that because it’s sin(t-2) which is the negative, we reflect the sin graph against the x-axis so the max value becomes -1.
But with another qs
P=17.4 2sin(0.7t-3) maximum value is when sin(0.7t-3)=1 which gives £19.40

Or does this depend on the context of the question given? if so how do you identify when to use the maximum or minimum as -1 or 1
It’s not always 1 or -1. But you can find out the maximum/minimum of a trigonometric function by:

1)Differentiating the equation, setting the derivative equal to zero and find values such that this holds. Plug the appropriate value back into the original equation to get the maximum/minimum (if you want to check which value is specifically maximum or minimum, you can differentiate again. By plugging in the aforementioned values, if plugging in a value causes the second derivative to be greater than zero, then that value is minimum. If plugging in a value causes the second derivative to be less than zero, then that value is maximum.)

2)Initially finding the range of the trigonometric function then build up from there to find the range of the overall function. For P = 17.4 2sin(0.7t - 3), you know that sin(0.7t-3) is between 1 and -1. Therefore
2sin(0.7t-3) is between 2 and -2; therefore
17.4 2sin(0.7t-3) is between 19.4 and 15.4. We can obviously see that 19.4 is the maximum of P (i.e when sin(0.7t - 3) is 1) in this case.

EDIT: You can ignore this post. The posts above are probably clearer and better.
Last edited by GrayestOwl0900; 2 years ago
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Jessica_rica
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#5
Report Thread starter 2 years ago
#5
(Original post by RDKGames)
P = 11.5 - 0.5sin(t-2)

In this expression you have (constsnt) TAKE AWAY (a function)

and since its take away, it means that in order maximise P you want to take away as little as possible from the constant.

The smallest value sin can take is -1 hence why this corresponds to the max.


On the other hand, the other function has (constant) PLUS (a function) where in order to maximise you want to add on as much as possible hence the value of sin is 1.
Thank u very much, I get it now,
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