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Trigonometry Help

Hi :smile:

I don't really need help on he question at ll. I just need help on the bit circled in blue. My teacher did mention that if cos was a multiple on both sides of the equation, I cannot cancel... he said something in the lines of "cos can equal 0"... can someone clarify this bit? Also can someone clarify that I cannot cancel sin for the reason in the box.

Also, should I be looking out for any other rules?
Tricky.jpg132.7KB
Original post by ps1265A
Hi :smile:

I don't really need help on he question at ll. I just need help on the bit circled in blue. My teacher did mention that if cos was a multiple on both sides of the equation, I cannot cancel... he said something in the lines of "cos can equal 0"... can someone clarify this bit? Also can someone clarify that I cannot cancel sin for the reason in the box.

Also, should I be looking out for any other rules?



I do not really understand what you are asking since you can cancel Sin(x) as the blue box says


If you have

x2=3xx^2 = 3x

and you cancel x you get

x=3x=3

However, if x=0 then the equations still works

So if you wish to divide both sides of an equation by something you have to consider if it can be 0


The alternative to cancelling is collecting and factorising

x2=3xx^2 = 3x

becomes

x2−3x=0x^2-3x = 0

giving

x(x−3)=0x(x-3) = 0

Giving x = 0 or x=3



So, in your question you can decide to cancel by Sin(x) as long as you think "can Sin(x) = 0" if it can then that is one of your solutions - if not go ahead and cancel

Since the angle is neither 0 nor 180 you know that Sin(x0 is not 0 so you are ok
Reply 2
Avatar for ps1265A
ps1265A
OP
14
Original post by TenOfThem
I do not really understand what you are asking since you can cancel Sin(x) as the blue box says


If you have

x2=3xx^2 = 3x

and you cancel x you get

x=3x=3

However, if x=0 then the equations still works

So if you wish to divide both sides of an equation by something you have to consider if it can be 0


The alternative to cancelling is collecting and factorising

x2=3xx^2 = 3x

becomes

x2−3x=0x^2-3x = 0

giving

x(x−3)=0x(x-3) = 0

Giving x = 0 or x=3



So, in your question you can decide to cancel by Sin(x) as long as you think "can Sin(x) = 0" if it can then that is one of your solutions - if not go ahead and cancel

Since the angle is neither 0 nor 180 you know that Sin(x0 is not 0 so you are ok


Fantastic explanation! Thanks so much!
Original post by ps1265A
Fantastic explanation! Thanks so much!


No problem
Reply 4
Avatar for ps1265A
ps1265A
OP
14
Original post by TenOfThem
I do not really understand what you are asking since you can cancel Sin(x) as the blue box says


If you have

x2=3xx^2 = 3x

and you cancel x you get

x=3x=3

However, if x=0 then the equations still works

So if you wish to divide both sides of an equation by something you have to consider if it can be 0


The alternative to cancelling is collecting and factorising

x2=3xx^2 = 3x

becomes

x2−3x=0x^2-3x = 0

giving

x(x−3)=0x(x-3) = 0

Giving x = 0 or x=3



So, in your question you can decide to cancel by Sin(x) as long as you think "can Sin(x) = 0" if it can then that is one of your solutions - if not go ahead and cancel

Since the angle is neither 0 nor 180 you know that Sin(x0 is not 0 so you are ok

I understand it, ignore what I've said below! My final question is, does this only need to be considered when cancelling? Not when multiplying, say times by cosθ in the question below... why isn't this a problem?
I've got a question related to what you've said:

(edited 9 years ago)
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