MYTUTOR SUBJECT ANSWERS

2443 views

Express cos(4x) in terms of powers of cos(x)

By quoting De Moivre's theorem, (r(cos(x) + isin(x)))n = rn(cos(nx) + isin(nx)), we can realise that cos(4x) is a result of the real parts of (cos(x) + isin(x))4

Using binomial expansion: (where c = cos(x) and s = sin(x))

(cos(x) + isin(x))4 = c4 + 4c3is + 6c2(is)2 + 4c(is)3 + (is)4

= c4 +4c3is - 6c2s2 - 4cis3 + s4

The real parts of this are c4, -6c2s2 and s4

Therefore, cos(4x) = c4 - 6c2s2 + s4

s2 = 1 - c2

6c2s2 = 6c2(1-c2) = 6c2 - 6c4

s4 = (1 - c2)2 = 1 - 2c2 + c4

By substituting these in:

cos(4x) = c4 - 6c2 + 6c4 + 1 - 2c2 + c4

= 8c4 - 8c2 + 1

Luis D. Mentoring Maths tutor, GCSE Maths tutor, Mentoring Geography ...

1 year ago

Answered by Luis, an A Level Further Mathematics tutor with MyTutor


Still stuck? Get one-to-one help from a personally interviewed subject specialist

62 SUBJECT SPECIALISTS

£20 /hr

Jaisal P.

Degree: Mathematics (Masters) - Durham University

Subjects offered: Further Mathematics , Maths

Further Mathematics
Maths

“Hello, my name is Jaisal. I'm studying Maths at Durham University, and I'm here to help you improve your Maths. ”

£20 /hr

Zhen X.

Degree: BSc Mathematics and Economics (Bachelors) - LSE University

Subjects offered: Further Mathematics , Maths+ 2 more

Further Mathematics
Maths
Mandarin
Economics

“About Me: I am a first year student at the London School of Economics studying BSc.Mathematics and Economics. I have always been interested in Mathematics and its application towards Economics. I am very patient and friendly. I have be...”

MyTutor guarantee

£26 /hr

Vandan P.

Degree: Physical Natural Sciences (Bachelors) - Cambridge University

Subjects offered: Further Mathematics , Science+ 6 more

Further Mathematics
Science
Physics
Maths
Chemistry
.STEP.
.MAT.
-Oxbridge Preparation-

“I am a second year undergraduate at Corpus Christi College Cambridge. I am studying Natural Sciences. In my first year I did Physics, Chemistry, Computer Science and Maths and passed with first class honours....”

About the author

Luis D.

Currently unavailable: for regular students

Degree: BA Geography (Bachelors) - Durham University

Subjects offered: Further Mathematics , Maths+ 1 more

Further Mathematics
Maths
Geography

“About Me:I am a first year geography student at Durham University, with a passion for the human side. Ever since primary school I have had the desire to understand how the world works, and I hope that this comes across in my tutorial...”

You may also like...

Posts by Luis

Express cos(4x) in terms of powers of cos(x)

How do I differentiate 3^2x?

What are the effects of TNCs is both the countries they operate in and their home countries?

Other A Level Further Mathematics questions

find general solution to: x(dy/dx) + 2y = 4x^2

What does it mean if two matrices are said to be commutative?

How do I differentiate tan(x) ?

Solve the inequality x^3 + x^2 > 6x

View A Level Further Mathematics tutors

Cookies:

We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss

mtw:mercury1:status:ok