Try using the sin^2x cos^2x = 1 rule to eliminate factors for the equation. You might be able to, say, hey rid of a cos^2x somewhere,or something.
(edited 5 years ago)
Original post by JustACoincidence
Try using the sin^2x cos^2x = 1 rule to eliminate factors for the equation. You might be able to, say, hey rid of a cos^2x somewhere,or something.
I don’t understand how to start any of the questions, I know the trig identities but how do I apply them in this instance
Bottom question should be quite simple.
For any/most "show that" questions, generally start with the expression on the LHS, then do the obvious algebra until you get the expression given to you on the RHS.
In this case, the 'obvious' thing is to square the bracket.
Top questions require a couple of steps at least.
First of all, you should be able to solve a trig eqn of the form
4sin(3x-20) = 0.7 , for example.
or
4cos(3x-20) = 0.7 ,
or
4tan(3x-20) = 0.7.
or
3sin^2(3x-20) - 4sin(3x-20) + 1 = 0
ie equations with just one trig function involved. Can you handle those?
When there's more than one trig function involved, you'll nearly always need to use a trig ident.
For any/most "show that" questions, generally start with the expression on the LHS, then do the obvious algebra until you get the expression given to you on the RHS.
In this case, the 'obvious' thing is to square the bracket.
Top questions require a couple of steps at least.
First of all, you should be able to solve a trig eqn of the form
4sin(3x-20) = 0.7 , for example.
or
4cos(3x-20) = 0.7 ,
or
4tan(3x-20) = 0.7.
or
3sin^2(3x-20) - 4sin(3x-20) + 1 = 0
ie equations with just one trig function involved. Can you handle those?
When there's more than one trig function involved, you'll nearly always need to use a trig ident.
Original post by JustACoincidence
Try using the sin^2x cos^2x = 1 rule to eliminate factors for the equation. You might be able to, say, hey rid of a cos^2x somewhere,or something.
sin2x + cos2x ≡ 1
Original post by Realdon66
Hi I am finding these questions difficult any help would be appreciated.
Attachment not found
If you have invested a little effort on it, this is pretty straightforward question. Have you covered double angle formulae? Do you know how to write tan(x) in terms of sine and cosine ?
(edited 5 years ago)
Original post by MathsLove
If you have invested a little effort on it, this is pretty straightforward question. Have you covered double angle formulae? Do you know how to write tan(x) in terms of sine and cosine ?
Agreed.
6 is straightfoward when using the right trig identity which above posters have recognised correctly.
7 may be 'harder' to spot, but it's simply double angle formula.
What are your workings so far?
7 doesn’t have to be double angle... you can spot it in first two lines!!
For 7- Try expanding the LHS see what you get, and use the identity sinx cosx=1
For 6 - use the identity sinx cosx=1 to re arrange some of the terms so that you have them just in terms of cos or sin, then compare with a quadratic and see what to do from there
Although I feel like I’m missjng something but why the above posters are talking about double angle formula, you can literally solve all these questions with the sin^2x cos^2x = 1 identity just rearranging it
For 7- Try expanding the LHS see what you get, and use the identity sinx cosx=1
For 6 - use the identity sinx cosx=1 to re arrange some of the terms so that you have them just in terms of cos or sin, then compare with a quadratic and see what to do from there
Although I feel like I’m missjng something but why the above posters are talking about double angle formula, you can literally solve all these questions with the sin^2x cos^2x = 1 identity just rearranging it
(edited 5 years ago)
Original post by timif2
Although I feel like I’m missjng something but why the above posters are talking about double angle formula, you can literally solve all these questions with the sin^2x cos^2x = 1 identity just rearranging it
Although I feel like I’m missjng something but why the above posters are talking about double angle formula, you can literally solve all these questions with the sin^2x cos^2x = 1 identity just rearranging it
Don't bother feeling like you're missing something. You're not.
These 3 qns are first year A-Level. None of that requires combination angles, or dble angle formulas.
Original post by begbie68
Bottom question should be quite simple.
For any/most "show that" questions, generally start with the expression on the LHS, then do the obvious algebra until you get the expression given to you on the RHS.
In this case, the 'obvious' thing is to square the bracket.
Top questions require a couple of steps at least.
First of all, you should be able to solve a trig eqn of the form
4sin(3x-20) = 0.7 , for example.
or
4cos(3x-20) = 0.7 ,
or
4tan(3x-20) = 0.7.
or
3sin^2(3x-20) - 4sin(3x-20) + 1 = 0
ie equations with just one trig function involved. Can you handle those?
When there's more than one trig function involved, you'll nearly always need to use a trig ident.
For any/most "show that" questions, generally start with the expression on the LHS, then do the obvious algebra until you get the expression given to you on the RHS.
In this case, the 'obvious' thing is to square the bracket.
Top questions require a couple of steps at least.
First of all, you should be able to solve a trig eqn of the form
4sin(3x-20) = 0.7 , for example.
or
4cos(3x-20) = 0.7 ,
or
4tan(3x-20) = 0.7.
or
3sin^2(3x-20) - 4sin(3x-20) + 1 = 0
ie equations with just one trig function involved. Can you handle those?
When there's more than one trig function involved, you'll nearly always need to use a trig ident.
Would you mind telling me the steps to get to the answer. In class, we’ve done trig identities but haven’t applied it to these types of questions (yet) Much appreciated!
Original post by Azim Patel
When dealing with proof questions, ... hence you get 1+2sinxcosx as required
Posting full solutions is against the forum rules.
Original post by Realdon66
Would you mind telling me the steps to get to the answer. In class, we’ve done trig identities but haven’t applied it to these types of questions (yet) Much appreciated!
It's kind of a shame that there's been a lot of bad advice and misquoting of identities in this thread, but at the end of the day, you only need to know the
Unparseable latex formula:
identity (and how to solve something like by writing ).\tex \sin^2 x + \cos^2 x = 1
So it's not like you have a lot of choices what to do - you just have to apply the identity..
Original post by Realdon66
Would you mind telling me the steps to get to the answer. In class, we’ve done trig identities but haven’t applied it to these types of questions (yet) Much appreciated!
After all the posts in this thread, have you made any progress? Please post everything you've tried even if you don't think it's correct.
Original post by Realdon66
Would you mind telling me the steps to get to the answer. In class, we’ve done trig identities but haven’t applied it to these types of questions (yet) Much appreciated!
I think I've given you a fair bit of help in my post #5.
I'll add more to what's already been given by me and others after you've shown/explained what you've attempted so far.
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