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# Maths, C3 help URGENT!!!! watch

1. Hey guyss, there's a question that comes up in almost ALL C3 edexcel papers and I just don't understand how to do them, could i pleaseee have some help! This is one example of the question:

a) Show that cos2X+sin2X can be written in the form Rsin(2X+a).
b) hence, solve, in the interval 0<X<180, the equation cos2X+sin2X=1, giving your answers as rational multiples of pie.

(this question is Also number 9 in the C3 edexcel book, page 112)

I can do part (a), but i cannot do part (b), pleasee can somebody tell me how! Thanks so much.
2. (Original post by inspiration9)
Hey guyss, there's a question that comes up in almost ALL C3 edexcel papers and I just don't understand how to do them, could i pleaseee have some help! This is one example of the question:

a) Show that cos2X+sin2X can be written in the form Rsin(2X+a).
b) hence, solve, in the interval 0<X<180, the equation cos2X+sin2X=1, giving your answers as rational multiples of pie.

(this question is Also number 9 in the C3 edexcel book, page 112)

I can do part (a), but i cannot do part (b), pleasee can somebody tell me how! Thanks so much.

you can do Rsin(2x+a)=1
Then sin(2x+a)=1/R
Then 2x+a=arcsin(1/R)

...

see if you can get it now!
3. what did you get for a? subsitute 2x+a=u and solve it like sinu=1/R and do siin inverse and substitute your values into 2x+a and find x
4. (Original post by thebassking)
you can do Rsin(2x+a)=1
Then sin(2x+a)=1/R
Then 2x+a=arcsin(1/R)

...

see if you can get it now!
Thankss, I can get up to there, the bit I have trouble with is using the quadrants and trying to work out what answers you get! It doesn't seem to make sense!
5. (Original post by inspiration9)
Thankss, I can get up to there, the bit I have trouble with is using the quadrants and trying to work out what answers you get! It doesn't seem to make sense!
what initial value of x do you get, if you dont know how to convert it to within the region look at a sin graph and use that to compare it to the x value you get.
6. (Original post by thebassking)
what initial value of x do you get, if you dont know how to convert it to within the region look at a sin graph and use that to compare it to the x value you get.
The equation i get is:
√2sin(2X+ 0.785) = 1

So then I end up with:
2X+0.785=0.785

Their answers are 0,45,180,225 (degrees) and that is the bit i dont understand, how from the previous step, you get to the answers!
7. (Original post by inspiration9)
Thankss, I can get up to there, the bit I have trouble with is using the quadrants and trying to work out what answers you get! It doesn't seem to make sense!
for sin the solutions will be pie-(the answer you obtain) and also adding and subtrating 360. do these methods within the range they ask for. is that what you meant ?
8. (Original post by inspiration9)
The equation i get is:
√2sin(2X+ 0.785) = 1

So then I end up with:
2X+0.785=0.785

Their answers are 0,45,180,225 (degrees) and that is the bit i dont understand, how from the previous step, you get to the answers!
edit sorry i didnt read you post properly, give me a sec
9. (Original post by lethal786)
for sin the solutions will be pie-(the answer you obtain) and also adding and subtrating 360. do these methods within the range they ask for. is that what you meant ?
Ye thats what I thought, But in this example, could you please show me how that works.
10. (Original post by inspiration9)
Hey guyss, there's a question that comes up in almost ALL C3 edexcel papers and I just don't understand how to do them, could i pleaseee have some help! This is one example of the question:

a) Show that cos2X+sin2X can be written in the form Rsin(2X+a).
b) hence, solve, in the interval 0<X<180, the equation cos2X+sin2X=1, giving your answers as rational multiples of pie.

(this question is Also number 9 in the C3 edexcel book, page 112)

I can do part (a), but i cannot do part (b), pleasee can somebody tell me how! Thanks so much.
cos2X+sin2X=1
i.e. Rsin(2X+a) = 1

sin(2x+a)= 1/R

Now, since you found the values of R and a you can change the domain of the function. ( remember when you took it in C2 last year?)

let 2x+a = y [ 2(0)+a <y< 2(180)+a]
Siny = 1/R

calculate the values of y. and then find then in terms of x. (x= (y-a)/2)

When you calculate the values of y add 360 to each answer and see if what you get is still inside the domain.

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