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# can't seem to factorise this? C3 watch

1. find all values for between 0 and 360
cot^2x = cosecx

i got cosec^2x - 1 = cosecx

so cosec^2x - cosecx - 1 = 0
and i cant factorise it
2. (Original post by ihatePE)
find all values for between 0 and 360
cot^2x = cosecx

i got cosec^2x - 1 = cosecx

so cosec^2x - cosecx - 1 = 0
and i cant factorise it
3. It doesn't factorise nicely.
4. (Original post by ihatePE)
find all values for between 0 and 360
cot^2x = cosecx

i got cosec^2x - 1 = cosecx

so cosec^2x - cosecx - 1 = 0
and i cant factorise it
Indeed, you can't. (well, nicely) You have a quadratic in , so you can use the quadratic formula, or complete the square.
5. Yes, not all CAST questions will factorise nicely and you will have to dig back to GCSE and AS maths to get everything you need to get a question right.
6. (Original post by Shaanv)
(Original post by B_9710)
It doesn't factorise nicely.
(Original post by _gcx)
Indeed, you can't. (well, nicely) You have a quadratic in , so you can use the quadratic formula, or complete the square.
(Original post by M4cc4n4)
Yes, not all CAST questions will factorise nicely and you will have to dig back to GCSE and AS maths to get everything you need to get a question right.
ok so ive tried completing the square and it didnt look nice so i did the quad formula, it's giving me decimals, which isnt nice either. considering my teacher said this is one of the oldest paper so it's supposed to be nicer, it's making me lose sleep
7. (Original post by ihatePE)
ok so ive tried completing the square and it didnt look nice so i did the quad formula, it's giving me decimals, which isnt nice either. considering my teacher said this is one of the oldest paper so it's supposed to be nicer, it's making me lose sleep
8. What did it look like when you completed the square?
9. (Original post by _gcx)
so the quad formula looks like this

(1+rt5) / 2 = 1.6
and
(1-rt5) / 2 = -0.6

so cosecx = 1.6 or -0.6

therefore sinx = 1/1.6 or -1/0.6

which looks weird so im not sure if its right
10. (Original post by ihatePE)
so the quad formula looks like this

(1+rt5) / 2 = 1.6
and
(1-rt5) / 2 = -0.6

so cosecx = 1.6 or -0.6

therefore sinx = 1/1.6 or -1/0.6

which looks weird so im not sure if its right
That's fine but watch your rounding. (try not to round until your final answer, it may/is likely to result in inaccuracies so if your answer is slightly off, that'll be the culprit) Now consider and . One will yield no solutions.
11. (Original post by ihatePE)
so the quad formula looks like this

(1+rt5) / 2 = 1.6
and
(1-rt5) / 2 = -0.6

so cosecx = 1.6 or -0.6

therefore sinx = 1/1.6 or -1/0.6

which looks weird so im not sure if its right
So you can eliminate one answer for what reason?

Sinx = 0.625 and Sinx = -1.67 which one of these is impossible?
12. (Original post by _gcx)
That's fine but watch your rounding. (try not to round until your final answer, it may/is likely to result in inaccuracies so if your answer is slightly off, that'll be the culprit) Now consider and . One will yield no solutions.
thanks its all coming back to me now
13. (Original post by M4cc4n4)
So you can eliminate one answer for what reason?

Sinx = 0.625 and Sinx = -1.67 which one of these is impossible?
thanks, i've eliminated -1.67 as it's out of sinx range

just very weird ive never seen wjec give questions with long ass decimals before.

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