How do you find the minimum of the equation sin^2(x) + 4sin(x)?

MYTUTOR SUBJECT ANSWERS

Answers / Maths / A Level / How do you find the minimum of the equation sin^2(x) + 4sin(x)?

732 views

How do you find the minimum of the equation sin^2(x) + 4sin(x)?

The first step to solving this problem is to treat it as a normal quadratic equation; if you are struggling with comparing our equation to a normal quadratic, try substituting sin(x) = y into the equation as shown:

sin²(x) + 4sin(x) becomes y²+ 4y

Even though our equation does not equal 0 we can still use the 'complete the square' method to help us find the minimum, after applying this method our equation becomes:

(y + 2)² - 4

From this we can substitue y for sin(x), giving:

(sin(x) + 2)² - 4

To find the minimum of our equation we have to take in to account the fact that sin(x) has a range of -1 to 1, which limits (sin(x) + 2) to a range of 1 to 3.

From this you should be able to deduct that the smallest value of (sin(x) + 2)²- 4 is -3. This occurs when sin(x) = -1.

(-1 + 2)²- 4 = 1²- 4 = -3

Hence the minimum of sin²(x) + 4sin(x) is -3.

Kirsten S. GCSE Maths tutor, A Level Maths tutor, A Level Further Mat...

2 years ago

Answered by Kirsten, an A Level Maths tutor with MyTutor

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

423 SUBJECT SPECIALISTS

Vlad B. 13 Plus Maths tutor, 11 Plus Maths tutor, GCSE Maths tutor, ...

View profile

£20 /hr

Vlad B.

Degree: Mathematics (Masters) - Bath University

Subjects offered:Maths, Further Mathematics

“Hi! I am studying Mathematics at Bath University and I am passionate about teaching, and learning mathematics.”

MyTutor guarantee

| 1 completed tutorial

Save profile

Scott R. GCSE Maths tutor, 13 Plus Maths tutor, A Level Maths tutor,...

View profile

£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

5.0

51 reviews | 123 completed tutorials

Save profile

Anil L. GCSE Chemistry tutor, A Level Chemistry tutor, GCSE Maths tut...

View profile

£20 /hr

Anil L.

Degree: Chemical Engineering (Masters) - University College London University

Subjects offered:Maths, Physics+ 2 more

“Patient, friendly and approachable - my aim is to help you excel in your chosen area of study by aiding you in gaining an appreciation for what you are learning”

MyTutor guarantee

Save profile

See more A Level Maths tutors

About the author

View profile

Kirsten S.

Currently unavailable: for regular students

Degree: Mathematics (Masters) - Durham University

Subjects offered:Maths, Further Mathematics

“About Me:I'm a first year student at Durham University studying for a Masters degree in Mathematics. I've loved Maths and Science for as long as I can remember and I'm hoping my tutorials will inspire the same love and passion in you...”

MyTutor guarantee

| 8 completed tutorials

Save profile

Version:	3.49.9
Build:	5f485a18d000
Time:	2017-09-20T16:11:15Z

MYTUTOR SUBJECT ANSWERS

How do you find the minimum of the equation sin^2(x) + 4sin(x)?

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

423 SUBJECT SPECIALISTS

About the author

You may also like...

Other A Level Maths questions

One-to-one help is at your fingertips