MYTUTOR SUBJECT ANSWERS

344 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...

10 months ago

Answered by Andrew, who tutored A Level Maths with MyTutor


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

258 SUBJECT SPECIALISTS

£26 /hr

Joe C.

Degree: Mathematics (Masters) - Bristol University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“I'm a third year student at Bristol University studying a Masters Degree in Mathematics. I try to make my tutorials engaging, and tailor them to your individual needs so that we are working towards the grade you aspire to achieve! I'v...”

£20 /hr

Alex A.

Degree: Physics (Masters) - Manchester University

Subjects offered: Maths, Science+ 4 more

Maths
Science
Physics
Drama
Chemistry
-Personal Statements-

“Hi, I'm currently studying for a Masters Degree in Physics at the University of Manchester. I'm keen on all things Maths and Science related, as well as having interests ranging from Rock Climbing to Acting. I've always thought that a ...”

£20 /hr

Alexandra F.

Degree: Archaeology (Bachelors) - Glasgow University

Subjects offered: Maths, Religious Studies+ 2 more

Maths
Religious Studies
English
Chemistry

“I am currently a student at the University of Glasgow studying Maths and Archaeology. I am extremely passionate about science in general but more specifically, maths. I was lucky enough to have several excellent maths teachers through...”

MyTutor guarantee

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

What is the integral of ln(x)? Hint: use parts for this integration

The curve "y=6x-x^2" and the line "y=2x" intersect at the origin. At what other coordinate to they intersect?

Question 3 on the OCR MEI C1 June 2015 paper. Evaluate the following. (i) 200^0 (ii) (9/25)^(-1/2)

How do I find the maximum/minimum of a function?

View A Level Maths 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