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

MYTUTOR SUBJECT ANSWERS

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

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).

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

423 SUBJECT SPECIALISTS

Anuradha D. Mentoring -Personal Statements- tutor, GCSE Physics tutor...

View profile

£30 /hr

Anuradha D.

Degree: Physics (Masters) - Durham University

Subjects offered:Maths, Physics+ 4 more

“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 ...”

4.9

60 reviews | 179 completed tutorials

Save profile

Sophie H. A Level Maths tutor, GCSE Maths tutor

View profile

£24 /hr

Sophie H.

Degree: Mathematics (Masters) - Bristol University

Subjects offered: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.”

5.0

33 reviews | 70 completed tutorials

Save profile

£26 /hr

Ellie B.

Degree: Mathematics (Masters) - York University

Subjects offered:Maths, Physics+ 1 more

“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!”

5.2