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)?

677 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

325 SUBJECT SPECIALISTS

Ayusha A. A Level Maths tutor, GCSE Maths tutor, A Level Physics tuto...

View profile

£24 /hr

Ayusha A.

Degree: BEng electrical and electronics engineering (Bachelors) - Newcastle University

Subjects offered:Maths, Physics+ 1 more

“About me: I am a final year Electrical and Electronic Engineering student at Newcastle University. I took Mathematics, Further Mathematics, Chemistry and Physics as my A-level subjects. I did peer mentoring in university and also have...”

5.0

43 reviews | 266 completed tutorials

Save profile

Emma B. GCSE Maths tutor, A Level Maths tutor, 11 Plus Maths tutor, G...

View profile

£20 /hr

Emma B.

Degree: Mechanical Engineering (Masters) - Southampton University

Subjects offered:Maths, Physics+ 1 more

“A positive and bubbly tutor who will put 100% into helping your child succeed and discover their passion for learning!”

MyTutor guarantee

Save profile

Tadas T. A Level Maths tutor, GCSE Maths tutor, IB Maths tutor, A Lev...

View profile

£26 /hr

Tadas T.

Degree: MMathPhil Mathematics and Philosophy (Bachelors) - Oxford, St Anne's College University

Subjects offered:Maths, Further Mathematics + 3 more

“University of Oxford Maths and Philosophy student happy to help students learn and stay motivated!”

5.0

71 reviews | 121 completed tutorials

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:	3.47.1
Build:	245b6290c38f
Time:	2017-07-12T13:15:28Z

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

325 SUBJECT SPECIALISTS

About the author

You may also like...

Other A Level Maths questions

One-to-one help is at your fingertips