This discussion is now closed.

Check out other Related discussions

- Maclaurin series
- ..
- Binomial expansion
- OCR A level Further Maths Core Pure 1 - 22 May 2024 Exam chat
- Oxbridge Maths - Interview Questions
- Maclaurin olympiad & BMO
- AQA Alevel Further Maths Paper 2 Predictions
- Intermediate UKMT
- BMO Prep
- Hamilton olympiad
- IMC
- Bmo/smc ukmt
- Oxbridge math and ukmt/other math challenges
- Math at Cambridge
- Kings Maths school
- Maclaurin olympiad
- UKMT Intermediate Math Challenge 2024 - Discussion
- A level Maths question
- Edexcel A-level Further Mathematics Paper 2 (9FM0 02) - 3rd June 2024 [Exam Chat]
- A level maths Edexcel Binomial Expansion

find a polynomial up to degree 4 for sin(cosx)

this is what ive done so far:

cos x = 1- x^{2}/2 + x^{4}/24

sin x = x - x^{3}/6

when i put the expansion of cosx into that of sinx theres something beeing added onto the constant for every term. any ideas on how to get round this?

this is what ive done so far:

cos x = 1- x

sin x = x - x

when i put the expansion of cosx into that of sinx theres something beeing added onto the constant for every term. any ideas on how to get round this?

There's something being contributed to not just the constant, but the coefficent of x^2 and x^4 too because expanding out (1-x^{2}/2! + x^{4}/4!)^{n} will always give you a term with x^0, x^2 and x^4.

The way to work out the constant coefficent (and which can be extended to the other two terms) is to realise what you're adding together.

(1-x^{2}/2! + x^{4}/4!)^{n} will always have a constant term of 1 when expanded out. Everything else depends on x and n. So when you add together all the x^0 terms in sin's expansion you've got

1 - 1/3! + 1/5! - 1/7! + ....

Looks a hell of a lot like sin(1) to me

The way to work out the constant coefficent (and which can be extended to the other two terms) is to realise what you're adding together.

(1-x

1 - 1/3! + 1/5! - 1/7! + ....

Looks a hell of a lot like sin(1) to me

There was, but I removed it. Wrangler and I were talking on MSN about this question, and there was a slight confusion about if you were expanding about sin or cos's zero. The way you and I've discussed is the correct way

- Maclaurin series
- ..
- Binomial expansion
- OCR A level Further Maths Core Pure 1 - 22 May 2024 Exam chat
- Oxbridge Maths - Interview Questions
- Maclaurin olympiad & BMO
- AQA Alevel Further Maths Paper 2 Predictions
- Intermediate UKMT
- BMO Prep
- Hamilton olympiad
- IMC
- Bmo/smc ukmt
- Oxbridge math and ukmt/other math challenges
- Math at Cambridge
- Kings Maths school
- Maclaurin olympiad
- UKMT Intermediate Math Challenge 2024 - Discussion
- A level Maths question
- Edexcel A-level Further Mathematics Paper 2 (9FM0 02) - 3rd June 2024 [Exam Chat]
- A level maths Edexcel Binomial Expansion

Latest

Trending

Last reply 1 month ago

How do l find the min & max radius of a circle on an argand diagramMaths

2

4