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# C3 OCR trigonometry

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1. Hey.
I don`t understand when given an trigonometric expression how to find the minimum and max values as in question 8(iii).
https://7c95ed1f832973eac0c6e1a52b08...20C3%20OCR.pdf
What method needs to be used?, thanks in advance
2. (Original post by SamuelN98)
Hey.
I don`t understand when given an trigonometric expression how to find the minimum and max values as in question 8(iii).
https://7c95ed1f832973eac0c6e1a52b08...20C3%20OCR.pdf
What method needs to be used?, thanks in advance
Ok, basically it relies on the fact that cos (theta) oscillates between 1 and -1, thus you know that cos(4 theta) also oscillates between those values and when it equals 1 it is at a peak, thus maximum and when at -1 trough thus minimum.

Should have asked first but have you done the first part of 8ii? like express in terms of cos (4theta)?
3. I can't download/open the PDF so if you could attach it I will be able to give more specific advice.

For the normal y=cos(x) and y=sin(x) graphs, the max is 1 and the min is -1. Of course this can be changed if they are multiplies. So the maximum of 5cos(x) would be 5.

Consider how squaring the function would change the maximum/minimum.
4. (Original post by Mav1)
I can't download/open the PDF so if you could attach it I will be able to give more specific advice.

For the normal y=cos(x) and y=sin(x) graphs, the max is 1 and the min is -1. Of course this can be changed if they are multiplies. So the maximum of 5cos(x) would be 5.

Consider how squaring the function would change the maximum/minimum.
Here you go, thanks.
Attached Images
5. January 2012 QP - C3 OCR.pdf (71.8 KB, 28 views)
6. (Original post by Nish123)
Ok, basically it relies on the fact that cos (theta) oscillates between 1 and -1, thus you know that cos(4 theta) also oscillates between those values and when it equals 1 it is at a peak, thus maximum and when at -1 trough thus minimum.

Should have asked first but have you done the first part of 8ii? like express in terms of cos (4theta)?
Yeah, i did part (ii) and for part (iii) i got as far as cos4theta=1/2
7. (Original post by SamuelN98)
Yeah, i did part (ii) and for part (iii) i got as far as cos4theta=1/2
I am not sure where your = has come from, this is not an equation.
8. (Original post by Mav1)
I am not sure where your = has come from, this is not an equation.
What should i have done?
9. (Original post by SamuelN98)
What should i have done?
What did you get for k in part i?
10. Okay so the method you should follow is (I am using x instead of theta)

Rearrange the equation to get it in the form you found in part a) (hints are usually given earlier in questions)

Next rearrange the terms that aren't in the 4x form into cos^2(2x) - sin^2(2x). Recognize this?

Next group your final terms together and think when will it be a maximum value?
11. (Original post by SamuelN98)
Yeah, i did part (ii) and for part (iii) i got as far as cos4theta=1/2
Here you go First time uploading so took awhile, if there is any ambiguity then let me know

12. The picture was of 8iii, I am assuming you were fine with 8i.
13. (Original post by Mav1)
Okay so the method you should follow is (I am using x instead of theta)

Rearrange the equation to get it in the form you found in part a) (hints are usually given earlier in questions)

Next rearrange the terms that aren't in the 4x form into cos^2(2x) - sin^2(2x). Recognize this?

Next group your final terms together and think when will it be a maximum value?
(Original post by Nish123)
Here you go First time uploading so took awhile, if there is any ambiguity then let me know

Thanks to both of you for your help, .
What topic would this specific question, come under, so i can look for some notes on it?
14. (Original post by SamuelN98)
Thanks to both of you for your help, .
What topic would this specific question, come under, so i can look for some notes on it?
Not sure what topic but if you look at this link

http://www.physicsandmathstutor.com/...-level-core-3/

and scroll down to the OCR section there are notes, questions by topic, videos and past papers!

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