MYTUTOR SUBJECT ANSWERS

642 views

Show that the equation 5sin(x) = 1 + 2 [cos(x)]^2 can be written in the form 2[sin(x)]^2 + 5 sin(x)-3=0

First, we need to realise that we will be using the trigonometric identity sin(x)2 + cos(x)2 = 1

As our goal is to end up with an equation involving only sin, we will therefore substitue cos(x)2 with ( 1 - sin(x)2 ), giving

5sin(x) = 1 + 2(1-sin(x)2)

We then expand the brackets, getting

5sin(x) = 1 + 2 - 2sin(x)2

We want the final equation to equal 0, so we add make 1+2 equal 3 and subtract it from both sides of the equation:

5sin(x) -3 = -2sin(x)2

we then add 2sin(x)2 on both sides, achieving the wanted equation:

2sin(x)2 + 5sin(x) -3 =0

Santiago G. GCSE Maths tutor, A Level Maths tutor, GCSE Spanish tutor...

1 year ago

Answered by Santiago, an A Level Maths tutor with MyTutor


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

266 SUBJECT SPECIALISTS

Katrina M. IB Maths tutor, 13 Plus  Maths tutor, GCSE Maths tutor, A ...
£20 /hr

Katrina M.

Degree: Mathematics Bsc (Bachelors) - Exeter University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Further Mathematics
-Personal Statements-

“Hi, I am a patient, experienced and enthusiastic tutor ready to help each student reach their full potential.”

£26 /hr

Martyna S.

Degree: Neurotechnology (Masters) - Imperial College London University

Subjects offered:Maths, Science+ 4 more

Maths
Science
Chemistry
Biology
.BMAT (BioMedical Admissions)
-Personal Statements-

“PhD candidate in Bioengineering at Imperial College London. Long experience in effective tutoring!”

Aisling R. A Level Maths tutor, A Level Chemistry tutor
£24 /hr

Aisling R.

Degree: Chemistry (Bachelors) - Bristol University

Subjects offered:Maths, Chemistry

Maths
Chemistry

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

About the author

£20 /hr

Santiago G.

Degree: Computer Science with Management (Bachelors) - Edinburgh University

Subjects offered:Maths, Spanish+ 2 more

Maths
Spanish
Physics
Computing

“Hi! I'm Santi, and I'm studying Computer Science with Management at the University of Edinburgh. I have always enjoyed subjects likemaths, physics and computing, andI'm here to help in any way possible with the questions you may have...”

MyTutor guarantee

You may also like...

Posts by Santiago

Find the positive value of x such that log (x) 64 = 2

Show that the equation 5sin(x) = 1 + 2 [cos(x)]^2 can be written in the form 2[sin(x)]^2 + 5 sin(x)-3=0

What is batch processing?

Other A Level Maths questions

How to do Integration by Parts?

The curve C has equation y = x^3 - 2x^2 - x + 9, x > 0. The point P has coordinates (2, 7). Show that P lies on C.

Find the derivative of x^x

A curve has the equation y = x^4 - 8x^2 + 60x + 7. What is the gradient of the curve when x = 6?

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