MYTUTOR SUBJECT ANSWERS

632 views

Given that 5cos^2(x) - cos(x) = sin^2(x), find the possible values of cos(x) using a suitable quadratic equation.

First, need to get all the terms in the equation to be the same. Using the following identity, it is possible to achieve this:

sin2(x) + cos2(x) = 1

1 - cos2(x) = sin2(x)

Substituting this into the equation in the question:

5cos2(x) - cos(x) = 1 - cos2(x)

6cos2(x) - cos(x) - 1 = 0

Replace the term cos(x) with y:

6y2 - y - 1 = 0

Product = -6

Sum = -1

There numbers that satisfy this are -3 and 2. Therefore, the factorised form of the eqation is:

(2y - 1)(3y + 1) = 0

The roots of this equation are: y = cos(x) = -1/3 or 1/2. Therefore these are the possible values of cos(x).

Andrew B. GCSE Chemistry tutor, A Level Chemistry tutor, GCSE Maths t...

1 year ago

Answered by Andrew, who tutored A Level Maths with MyTutor


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

324 SUBJECT SPECIALISTS

PremiumTimothy N. A Level Design & Technology tutor, GCSE Design & Technolog...
£36 /hr

Timothy N.

Degree: Architecture and Environmental Engineering (Masters) - Nottingham University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Design & Technology
-Personal Statements-

“Hi there, I have a passion for helping students achieve, and believe that with my 200+ hours of experience, we will be able to surpass the grades you want!”

£20 /hr

Giorgos A.

Degree: Mechanical Engineering with Renewable Energy (Masters) - Edinburgh University

Subjects offered:Maths, Physics

Maths
Physics

“Feel rewarded helping younger students. Nobody is born knowing everything, life is a learning process and my aim is to help you achieve your goals.”

Trusted by schools

|  5 completed tutorials

£20 /hr

Shivani M.

Degree: Medicine (Bachelors) - Exeter University

Subjects offered:Maths, Chemistry+ 4 more

Maths
Chemistry
Biology
.UKCAT.
.BMAT (BioMedical Admissions)
-Medical School Preparation-

“I graduated with 5 A-levels last year and now study medicine at Exeter. I have mentored GCSE maths students for the last 2 years. I would love to hear from you!”

About the author

Andrew B.

Currently unavailable: until 01/09/2016

Degree: Chemistry (Masters) - Oxford, Keble College University

Subjects offered:Maths, Chemistry

Maths
Chemistry

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

MyTutor guarantee

You may also like...

Posts by Andrew

Explain how electricity is conducted through a metal. To gain full marks your answer must include a description of the structure and bonding in a metal.

Factorise and solve x^2 – 8x + 15 = 0

Given that 5cos^2(x) - cos(x) = sin^2(x), find the possible values of cos(x) using a suitable quadratic equation.

Identify the dehydration product or products of a) ethanol, b) button-2-ol

Other A Level Maths questions

Solve 4cos(2x )+ 2sin(2x) = 1 given -90° < x < 90°. Write 4cos(2x )+ 2sin(2x) in the form Rcos(2x - a), where R and a are constants.

When using the addition rule in probability, why must we subtract the "intersection" to find the "union" with the Addition Rule?

Find the value of: d/dx(x^2*sin(x))

Form the differential equation representing the family of curves x = my , where, m is arbitrary constant.

View A Level 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