C3 OCR trigonometry

Hey.
I don`t understand when given an trigonometric expression how to find the minimum and max values as in question 8(iii).
https://7c95ed1f832973eac0c6e1a52b08181fd38e50f6.googledrive.com/host/0B1ZiqBksUHNYcWYycEk2VmM2b00/January%202012%20QP%20-%20C3%20OCR.pdf
What method needs to be used?, thanks in advance :smile:

Reply 1

Nish123

Original post by SamuelN98

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)?

(edited 7 years ago)

Reply 2

username1914251

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.

Reply 3

SamuelN98

Original post by Mav1

Here you go, thanks.

January 2012 QP - C3 OCR.pdf73.5KB

Reply 4

SamuelN98

Original post by Nish123

Yeah, i did part (ii) and for part (iii) i got as far as cos4theta=1/2

Reply 5

username1914251

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.

Reply 6

SamuelN98

Original post by Mav1

I am not sure where your = has come from, this is not an equation.

What should i have done?

Reply 7

username1914251

Original post by SamuelN98

What should i have done?

What did you get for k in part i?

Reply 8

username1914251

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?

(edited 7 years ago)

Reply 9

Nish123

Original post by SamuelN98

Yeah, i did part (ii) and for part (iii) i got as far as cos4theta=1/2

Here you go :smile:

First time uploading so took awhile, if there is any ambiguity then let me know :wink:

(edited 7 years ago)

Reply 10

Nish123

The picture was of 8iii, I am assuming you were fine with 8i.

Reply 11

SamuelN98

Original post by Mav1

Original post by Nish123

Here you go :smile:

First time uploading so took awhile, if there is any ambiguity then let me know :wink:

Thanks to both of you for your help, :smile:

.
What topic would this specific question, come under, so i can look for some notes on it?

Reply 12

username1914251

Original post by SamuelN98

Thanks to both of you for your help, :smile:

.
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/maths-revision/a-level-core-3/

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