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# Trig question watch

1. Im going through C3 and something twisted my brain. We are told that you can't divide by sin x or cos x in the interval 0 to 360 because it may be 0 making the equation undefined however in many cases when we have sinx=cos x we solve for tan x = 1 in that interval and when i check the solution bank they sometimes multiply both sides by cos x even tho the interval is 0 to 180.
The question here is when can I know whether or not to divide by cos x or sin x?
Because i havent been able to find a solid rule for that
2. (Original post by Tirawi19)
Im going through C3 and something twisted my brain. We are told that you can't divide by sin x or cos x in the interval 0 to 360 because it may be 0 making the equation undefined however in many cases when we have sinx=cos x we solve for tan x = 1 in that interval and when i check the solution bank they sometimes multiply both sides by cos x even tho the interval is 0 to 180.
The question here is when can I know whether or not to divide by cos x or sin x?
Because i havent been able to find a solid rule for that
I'll be working with the range for this answer. If you want to be really careful, when you have the equation , you can separate it into two cases: when and when . If , then , but and so there are no solutions when . Now consider the case when . When this is the case, you can divide the equation by and proceed as normal. I think it's great that you're thinking carefully about what you're doing, and whether it's valid or not.
3. (Original post by Tirawi19)
Im going through C3 and something twisted my brain. We are told that you can't divide by sin x or cos x in the interval 0 to 360 because it may be 0 making the equation undefined however in many cases when we have sinx=cos x we solve for tan x = 1 in that interval and when i check the solution bank they sometimes multiply both sides by cos x even tho the interval is 0 to 180.
The question here is when can I know whether or not to divide by cos x or sin x?
Because i havent been able to find a solid rule for that
Good question!

If a trig function could be equal to 0 in an equation then you should not divide by it e.g.

If you divide by you get

But if you factorise instead you get

Which leads to as well as . So dividing by loses the solution .

If you're dividing an equation by cos to give tan, for the majority of occasions you'll be fine since can't be equal to 0 in your equation. But it's always worth checking.

So for , it is not possible for to be 0 and for that to satisfy the eqaution (think about this and let us know if you need more explanation). So it's fine to divide the equation by .
4. (Original post by I hate maths)
I'll be working with the range for this answer. If you want to be really careful, when you have the equation , you can separate it into two cases: when and when . If , then , but and so there are no solutions when . Now consider the case when . When this is the case, you can divide the equation by and proceed as normal. I think it's great that you're thinking carefully about what you're doing, and whether it's valid or not.
Thanks alot u really helped me get through so much !

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