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


£20 /hr

Praveenaa K.

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths, Science+ 4 more

Further Mathematics
-Personal Statements-

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

£36 /hr

Henri F.

Degree: Aerospace Engineering PhD Spacecraft Control (Doctorate) - Bristol University

Subjects offered:Maths, Physics+ 4 more

Further Mathematics
Extended Project Qualification

“Aerospace Engineering PhD candidate in spacecraft control with 7 years of experience in tutoring.”

£26 /hr

Priya L.

Degree: Economics (Bachelors) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

Further Mathematics

“My goal is to elevate the confidence of students by ensuring they truly understand Maths at GCSE and A Level”

About the author

£20 /hr

Elliot B.

Degree: Mathematics (Masters) - Durham University

Subjects offered:Maths, Further Mathematics

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

State the trigonometric identities for sin2x, cos2x and tan2x

Solve x^2 + 8x +3 = 0 by completing the square.

how to integrate by parts

What is the meaning of sine and cosine?

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