MYTUTOR SUBJECT ANSWERS

778 views

Find cos4x in terms of cosx.

As with any question involving sines and cosines, consider complex numbers as a likely way to find the answer. For this particular kind of question, where sin/cos of a multiple of x is needed in terms of sinx/cosx, or vice versa, the complex number representation z = cosx + isinx must be expanded in two ways. 

Firstly, expand using de Moivre's Theorem:

z = cosx + isinx

z4 = (cosx + isinx)4 =  cos4x + sin4x

Then, expand using the binomial expansion formula to get powers of cosx:

z4 = (cosx + isinx)4 = cos4x + 4icos3xsinx + 6i2cos2xsin2x + 4i3cosxsin3x + i4sin4x

                               = cos4x + 4icos3xsinx - 6cos2xsin2x - 4icosxsin3x + sin4x

Equate the real parts of both expansions to get cos equivalence:

cos4x = cos4x - 6cos2xsin2x + sin4x

Use cos2x + sin2x = 1 as a substitution:

cos4x = cos4x - 6cos2x(1-cos2x) + (1-cos2x)2

          = 8cos4x - 8cos2x + 1

Ellie S. IB Maths tutor, GCSE Maths tutor, IB Physics tutor, GCSE Phy...

12 months ago

Answered by Ellie, an IB Maths tutor with MyTutor


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

37 SUBJECT SPECIALISTS

£22 /hr

Ana S.

Degree: Physics (Bachelors) - Oxford, Balliol College University

Subjects offered:Maths, Physics+ 3 more

Maths
Physics
.STEP.
.PAT.
-Oxbridge Preparation-

“A friendly and understanding tutor with three years experience in school clubs, summer camps and private tutoring.”

£20 /hr

Ayokansola A.

Degree: Civil and Structural Engineering with a Year in Industry (Masters) - Sheffield University

Subjects offered:Maths, Spanish+ 4 more

Maths
Spanish
Science
Physics
English
Economics

“About Me: Hello! I am a Civil Engineering student at the University of Sheffield. I have always had a natural incline towards all things Maths and Science, so without a doubt, my genuine passion for the subjects’ I am offering will be...”

£22 /hr

Hanumanth Srikar K.

Degree: Maths and Economics (Bachelors) - LSE University

Subjects offered:Maths, German+ 3 more

Maths
German
Further Mathematics
Economics
Chemistry

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

About the author

Ellie S.

Currently unavailable: for new students

Degree: Physics (Bachelors) - Oxford, Lady Margaret Hall University

Subjects offered:Maths, Physics+ 3 more

Maths
Physics
Further Mathematics
.PAT.
-Personal Statements-

“My Background: Hi! I'm Ellie, I'm 19, and I'm a Physics student at Oxford University. My strengths aremaths and physics, although I did a number of different subjects in sixth form, so I am also very familiar with Latin, English, and ...”

MyTutor guarantee

You may also like...

Posts by Ellie

A cricketer throws a ball vertically upwards so that the ball leaves his hands at a speed of 25 m/s. Calculate the maximum height reached by the ball, the time taken to reach max. height, and the speed of the ball when it is at 50% max. height.

Differentiate y = e^(x^2 - 3x).

Find cos4x in terms of cosx.

The tip of each prong of a tuning fork emitting a note of 320Hz vibrates in SHM with an amplitude of 0.50mm. What is the speed of each tip when its displacement is zero?

Other IB Maths questions

Factorise z^3+1 into a linear and quadratic factor. Let y=(1+i√3)/2. Show that y is a cube root of -1. Show that y^2=y-1. Find the value of (1-y)^6.

Given the function y=f(x), where f(x)=(e^x-e^(-x))/2, find its inverse f'(x).

Why is (-1)*(-1)=1?

When the polynomial 3x^3 +ax+ b is divided by x−2 , the remainder is 2, and when divided by x +1 , it is 5. Find the value of a and the value of b.

View IB Maths tutors

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

mtw:mercury1:status:ok