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# Trig equations watch

1. For a question that says solve for between the interval 0 and 360.

Can I start by multiplying by 2? As this will lead me to a different answer (from what I've tried unless I did it wrong) or do I just have to factorise keeping the in there?

Thanks!
2. (Original post by Secret.)
For a question that says solve for between the interval 0 and 360.

Can I start by multiplying by 2? As this will lead me to a different answer (from what I've tried unless I did it wrong) or do I just have to factorise keeping the in there?

Thanks!
I'd start by writing cos2 as 1 - sin2
3. (Original post by Secret.)
For a question that says solve for between the interval 0 and 360.

Can I start by multiplying by 2?
Why would you multiply by 2

That would just give you
4. (Original post by TenOfThem)
Why would you multiply by 2

That would just give you

Ah okay thanks! I thought the x2 would get rid of the 2 in thanks for clearing that up
5. make cos^2x= 1-sin^2x (x replaces 1/2 theta)

you get sin^2x+sinx=0

sinx(sinx+1)=0

you get sin(1/2 theta)= 0,-1 then just multiply your answers by two and use the ones that fit in the interval.

Once again I think i might be wrong but lets hope im not lol

for

0, 180 and 360
-90 and 270

Now as the range in the question said

I cancel of the 360 in the top, however I was taught that you 'wind back a cycle' of 180 from answers outside the range, would the 360 not be within range?
Or does the answers have to be within range as when they are
I understand that the -90 would be cancelled but if I am supposed to wind back a cycle of 180 for 360 and 270 wouldn't they be within range?

I hope that makes sense and thanks!
7. (Original post by Secret.)

for

0, 180 and 360
-90 and 270

Now as the range in the question said

I cancel of the 360 in the top, however I was taught that you 'wind back a cycle' of 180 from answers outside the range, would the 360 not be within range?
Or does the answers have to be within range as when they are
I understand that the -90 would be cancelled but if I am supposed to wind back a cycle of 180 for 360 and 270 wouldn't they be within range?

I hope that makes sense and thanks!
If

and

then you have 2 solutions.
8. (Original post by Secret.)
Ah okay thanks! I thought the x2 would get rid of the 2 in thanks for clearing that up
Nope, because cos() and sin() are functions. If you multiply, you just get a multiple of that function.

If you still need convincing, just consider some simple function such as:

f(x) = x + 2

You need to solve for the whole parameter passed to the function before you can fiddle with it to end up with just a part of it.

i.e. in this case, solve for theta/2, then multiply to find theta, as other's have explained.

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Updated: March 25, 2013
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