MYTUTOR SUBJECT ANSWERS

356 views

Solve the equation; 4 cos^2 (x) + 7 sin (x) – 7 = 0, giving all answers between 0° and 360°.

4 cos2 (x) + 7sin (x) – 7 = 0      (1)

Using the identity sin2 (x) + cos2 (x) = 1,

rearrange to give; cos2 (x) = 1 - sin2 (x)     (2)

Sub (2) into (1)...

Giving;  4 ( 1 - sin2 (x) ) + 7sin (x) - 7 = 0

Expand brackets; 4 - 4sin2 (x) + 7sin (x) - 7 = 0

Simplify; 7sin (x) - 4sin2 (x) - 3 = 0

Let sin(x) = A and treat as a quadratic;

7A - 4A2 - 3 = 0

- (4A - 3)(A - 1) = 0

4A - 3 = 0 or A - 1 = 0

4A = 3  or A = 1

A = 3/4

However, we already have defined A = sin (x), therefore we must not stop here, but set A = sin (x) and solve for x as follows:

sin (x) = 3/4 or sin (x) = 1

x = sin-1 (3/4) or x = sin-1 (1)

x = 48.6° and (180 - 48.6)° [1] or 90°

x = 48.6° and 131° or 90.0° (to 3 significant figures)

[1]: Note that we take 180° - angle, as for x in sin (x) between 0° and 180° is symmetrical around 90°​. If x was between 180° and 360°, we'd do (360 - x) if 180 < x < 270 and (180 + x) if 270 < x < 360.

Connor S. GCSE Maths tutor, A Level Maths tutor, GCSE Physics tutor, ...

6 months ago

Answered by Connor, an A Level Maths tutor with MyTutor


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

269 SUBJECT SPECIALISTS

Sahil M. A Level Biology tutor, GCSE Biology tutor, A Level Chemistry...
£22 /hr

Sahil M.

Degree: Medicine (Bachelors) - Manchester University

Subjects offered:Maths, Spanish+ 3 more

Maths
Spanish
Chemistry
Biology
-Medical School Preparation-

“Hello! My name is Sahil and I am currently a medical student at the University of Manchester. I am really looking forward to tutoring you in Spanish, Chemistry, Biology or Maths as well as trying to help you during the difficult proce...”

£24 /hr

Anahita G.

Degree: Maths and Economics (Bachelors) - York University

Subjects offered:Maths, Science+ 3 more

Maths
Science
Economics
Chemistry
.TSA. Oxford.

“I am a maths and economics student at the University of York. I have always loved logical and analytical subjects, for example Maths and the Sciences. I also particularly enjoy economics as there are countless ways to analyse and conc...”

£22 /hr

Mark H.

Degree: Mathematics MMath (Masters) - Manchester University

Subjects offered:Maths, Physics+ 1 more

Maths
Physics
Further Mathematics

“Hello there, I'm Mark and I study Mathematics at the University of Manchester! Let me help you achieve your best! ”

About the author

£20 /hr

Connor S.

Degree: Physics (Masters) - Durham University

Subjects offered:Maths, Physics

Maths
Physics

“About Me: I am a physics student at Durham University. I have had a passion for physics instilled in me from many inspirational teachers over the years, something I desire to do also to my students. I have had experience in tutoring ...”

MyTutor guarantee

You may also like...

Posts by Connor

Explain in terms of the motion of the molecules of the gas why the volume of gas must increase if the pressure is to remain constant as the gas is heated.

Solve the equation; 4 cos^2 (x) + 7 sin (x) – 7 = 0, giving all answers between 0° and 360°.

Other A Level Maths questions

Find dy/dx of 5x^2 + 2y^3 +8 =17.

How to differentiate tan(x)?

How do I integrate sin^2(x)?

How do I find the maxima and minima of a function?

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