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Mathematics: Post your doubts here!

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i have nearly done all the questions and only this one bothered me :/ why 360?
Pretty simple actually, I prefer making a diagram like this:
_20140503_172317.JPG
As you can see the letters, the S T and C stand for sin cos tan, these functions are positive in these ranges of angles while in A, all three are positive. When you look at your question, you have tan@ = - 7
I prefer to use this trick, take the inverse of positive 7 instead of negative seven and then look at the angle that you get. Like here you get: 81.67 degrees
Now use the diagram above and see in which ranges will tan@ have negative values, so you will see that happens in the 90 to 180 interval and the 270 to 360 interval.
Now, just use the formulas I have provided in the brackets and you will get your answer :D
Memorise this, it'll be extremely helpful ;)
 
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You technically copied what was written in the mark scheme. I would write something like this:
tan^2@ - sin^2@ is always greater than zero for the values of theta between 0 to 90. Hence,
tan^2@ - sin^2@ > 0
tan^2@ > sin^2@
tan@ > sin@
Now that I think about it, you did write everything that is required plus it is just worth one mark so you aren't expected to do much working. So that should be enough :p
Haya Ahmed Here's your question 1 part 2

and as for question 4, just look at the range, it is from 0 to 1080. So just understand that the wave cycle keeps repeating itself so how many answers did you get for 0 to 360, multiply it by how many cycles further the range has been extended and you can find that out by dividing 1080 by 360 that'll give you, 3. So 3 into the number of answers you had for 0 to 360. That will be your final answer.
 
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Haya Ahmed Here's your question 1 part 2

and as for question 4, just look at the range, it is from 0 to 1080. So just understand that the wave cycle keeps repeating itself so how many answers did you get for 0 to 360, multiply it by how many cycles further the range has been extended and you can find that out by dividing 1080 by 360 that'll give you, 3. So 3 into the number of answers you had for 0 to 360. That will be your final answer.
OMG .. thanks a lot bro you're awesome .. THANKS AGAIN !! ^_^
 
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Pretty simple actually, I prefer making a diagram like this:
View attachment 40958
As you can see the letters, the S T and C stand for sin cos tan, these functions are positive in these ranges of angles while in A, all three are positive. When you look at your question, you have tan@ = - 7
I prefer to use this trick, take the inverse of positive 7 instead of negative seven and then look at the angle that you get. Like here you get: 81.67 degrees
Now use the diagram above and see in which ranges will tan@ have negative values, so you will see that happens in the 90 to 180 interval and the 270 to 360 interval.
Now, just use the formulas I have provided in the brackets and you will get your answer :D
Memorise this, it'll be extremely helpful ;)
I use the same thing actually but i didn't know to use this for negative values
Thanks :D
 
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Pretty simple actually, I prefer making a diagram like this:
View attachment 40958
As you can see the letters, the S T and C stand for sin cos tan, these functions are positive in these ranges of angles while in A, all three are positive. When you look at your question, you have tan@ = - 7
I prefer to use this trick, take the inverse of positive 7 instead of negative seven and then look at the angle that you get. Like here you get: 81.67 degrees
Now use the diagram above and see in which ranges will tan@ have negative values, so you will see that happens in the 90 to 180 interval and the 270 to 360 interval.
Now, just use the formulas I have provided in the brackets and you will get your answer :D
Memorise this, it'll be extremely helpful ;)
http://papers.xtremepapers.com/CIE/...S Level/Mathematics (9709)/9709_s12_qp_13.pdf
question 4i) how to do this, by your trick ? :)
 
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Sin2x + 3cos2x=0
sin2x=-3cos2x
sin2x/cos2x= - 3
tan2x= - 3
now tan-1 (3) = 71.56....Since tanx is -ve , x lies in either 2nd or 4th quadrant.Secondly,you see that range is from 0 to 360 and you are finding for 2x.So,
2x=(180-71.56) , (360-71.56) ,(540-71.56) , (720-71.56) as u know: 2nd quad is (180-x) and 4th is (360-x). Then u can see that x has values in 2nd revolution.So,2nd quad is (540-x) and 4th is (720-x)
Then u can easily find x by dividing all values of 2x by 2.Show all values to 2 dp.I hope i was helpful :/
 
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Sin2x + 3cos2x=0
sin2x=-3cos2x
sin2x/cos2x= - 3
tan2x= - 3
now tan-1 (3) = 71.56....Since tanx is -ve , x lies in either 2nd or 4th quadrant.Secondly,you see that range is from 0 to 360 and you are finding for 2x.So,
2x=(180-71.56) , (360-71.56) ,(540-71.56) , (720-71.56) as u know: 2nd quad is (180-x) and 4th is (360-x). Then u can see that x has values in 2nd revolution.So,2nd quad is (540-x) and 4th is (720-x)
Then u can easily find x by dividing all values of 2x by 2.Show all values to 2 dp.I hope i was helpful :/
Yep! That's it although I have to say, this is not at all my trick (I ain't that clever :oops:) All credit goes to my genius math teacher in school mashaAllah:LOL:
 
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Sin2x + 3cos2x=0
sin2x=-3cos2x
sin2x/cos2x= - 3
tan2x= - 3
now tan-1 (3) = 71.56....Since tanx is -ve , x lies in either 2nd or 4th quadrant.Secondly,you see that range is from 0 to 360 and you are finding for 2x.So,
2x=(180-71.56) , (360-71.56) ,(540-71.56) , (720-71.56) as u know: 2nd quad is (180-x) and 4th is (360-x). Then u can see that x has values in 2nd revolution.So,2nd quad is (540-x) and 4th is (720-x)
Then u can easily find x by dividing all values of 2x by 2.Show all values to 2 dp.I hope i was helpful :/
Then, it does not matter at all if there is - sign or +ve sign ?
 
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