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# C4 R-alpha Method

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1. Hi
After expressing an equation in the form RSin(x-alpha), how do i find the 'greatest and least possible values'

I have 2sinx-3cosx = rt13(x-0.983)

Write down the greatest and least possible values of 1 + 2sinx-3cosx

The write down bit signifies to me that this shouldnt take too long.

im not sure what to do...???
thanks
2. (Original post by starwarsjedi123)
Hi
After expressing an equation in the form RSin(x-alpha), how do i find the 'greatest and least possible values'

I have 2sinx-3cosx = rt13(x-0.983)

Write down the greatest and least possible values of 1 + 2sinx-3cosx

The write down bit signifies to me that this shouldnt take too long.

im not sure what to do...???
thanks
Given something of the form RSin(x-alpha):

What is the maximum value that sin(x) can take for any value of x?

Hence what is the maximum value that sin(x-alpha) can take for any values of x or alpha?

Hence what is the maximum value of..
3. The maximum value is 1? and the minimum is -1?

So maximum of sin(x-alpha) would be x-alpha=1 ??
4. (Original post by starwarsjedi123)
The maximum value is 1? and the minimum is -1?

So maximum of sin(x-alpha) would be x-alpha=1 ??
If you quote people like so, they can see that you've replied

Correct, max is 1 and min is -1 for sinx.

For sin(x-alpha), this is also the same. For any values of x and alpha, we can define some value c = x - alpha, giving sin(x-alpha) = sin(c), which looks just like sinx so the maximum is still 1 and -1.

With that in mind, you have the R to worry about. So the max of Rsin(x-alpha) is..
5. its simply rt13 is it not??? rt13 stretches sinx parallel to y axis??

so the answer to my original question is simply 1+rt13 and 1-rt13??

(Original post by SeanFM)
If you quote people like so, they can see that you've replied

Correct, max is 1 and min is -1 for sinx.

For sin(x-alpha), this is also the same. For any values of x and alpha, we can define some value c = x - alpha, giving sin(x-alpha) = sin(c), which looks just like sinx so the maximum is still 1 and -1.

With that in mind, you have the R to worry about. So the max of Rsin(x-alpha) is..
6. (Original post by starwarsjedi123)
its simply rt13 is it not??? rt13 stretches sinx parallel to y axis??

so the answer to my original question is simply 1+rt13 and 1-rt13??
Correct well done.

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