MYTUTOR SUBJECT ANSWERS

870 views

How do I solve equations like 3sin^2(x) - 2cos(x) = 2

To solve equations like this we need to get the equation in terms of one trigonometric function, ie one of sin(x), cos(x) or tan(x)

It is usually easiest to get everything in terms of whatever the linear part of the equation is, in this case cos(x).

To do this we use that sin2(x) + cos2(x) = 1. Since we're trying to get rid of the sin2(x) part of the equation we rearrange this to get that sin2(x) = 1 - cos2(x)

We substitute this into the equation 3sin2(x) - 2cos(x) = 2

This gives 3(1 - cos2(x)) - 2cos(x) = 2

This then becomes 3 - 3cos2(x) - 2cos(x) = 2

which we can rearrange to 3cos2(x) + 2cos(x) - 1 = 0

Now that we have an equation just in terms of one trigonometric function , here cos(x), we can just replace it with some letter, say y

Thus this is just 3y2 + 2y - 1 = 0. We can solve this with the usual quadratic equation, giving y = -1 and y = 1/3. As y = cos(x) this is just cos(x) = -1 and cos(x) = 1/3. To find x we then just solve these in the usual way

Elliot B. A Level Maths tutor, A Level Further Mathematics  tutor, GC...

2 years ago

Answered by Elliot, an A Level Maths tutor with MyTutor


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

269 SUBJECT SPECIALISTS

£22 /hr

Sam F.

Degree: Economics with Placement (Bachelors) - Bath University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Extended Project Qualification
Economics

“Studying for BSc Hons Economics, A level economics, maths and physics. Able to tutor GCSE/AS/A2 Economics, Maths and GCSE physics! ”

£20 /hr

Ioannis P.

Degree: Computer Science (Bachelors) - Warwick University

Subjects offered:Maths

Maths

“Maths and Computer Science are both my passion. Having tutored students in the past, they think that my methods seem very intuitive and natural; you will too.”

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

Elliot B.

Degree: Mathematics (Masters) - Durham University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

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

MyTutor guarantee

You may also like...

Other A Level Maths questions

What is the derivative of x^x

How do you integrate 3x^2 - 6x + 5 (wrt x)?

How do I integrate ln(x)

Differentiate y = (6x-13)^3 with respect to x

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