718 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).

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

#### 423 SUBJECT SPECIALISTS

£30 /hr

Degree: Physics (Masters) - Durham University

Subjects offered:Maths, Physics+ 4 more

Maths
Physics
Music
Further Mathematics
Chemistry
-Personal Statements-

“Hello everyone! My name is Anuradha (you can call me Anu), and I am a Physics Undergrad at Durham. I have always had a “thing” for science and am so pleased to be studying it – and hope that I can give you all the support you need to ...”

£24 /hr

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I’ll help anyone finding maths hard. I still struggle now, it's not meant to be easy! Be at my tutorial or (c^2-a^2) <- a maths joke, I apologise.”

£26 /hr

Degree: Mathematics (Masters) - York University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“I study Maths at York University; I chose York because I loved the lecturers, they made maths fun and easy- that's what I hope to do with all my students!”

Currently unavailable: until 01/09/2016

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

Subjects offered:Maths, Chemistry

Maths
Chemistry

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

Show that 2sin(2x)-3cos(2x)-3sin(x)+3=sin(x)(4cos(x)+6sin(x)-3)

How do you take the derivative of a^x ?

Consider the functions f and g where f (x) = 3x − 5 and g (x) = x − 2 . (a) Find the inverse function, f^−1 . (b) Given that g^−1(x) = x + 2 , find (g^−1 o f )(x) . (c) Given also that (f^−1 o g)(x) = (x + 3)/3 , solve (f^−1 o g)(x) = (g^−1 o f)(x)

Solve \$\color{orange}{a}x^2 - \color{blue}{b}x + \color{green}{c} = 0\$

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