How do I solve the equation "2cos(x) = sin(2x), for 0 ≤ x ≤ 3π"?

The key to solving this equation is realizing that sin(2x) can be written in terms of sin(x) and cos(x) using a double-angle formula. (With trigonometric problems similar to this one, you should always check if any trigonometric identites like the double-angle formulae can be used, as these can often help you.)

Using your IB formula booklet, you will see that the double-angle formula for sine is:

sin(2x) = 2sin(x)cos(x) 

Therefore, we can rewrite the given equation from:

2cos(x) = sin(2x)


2cos(x) = 2sin(x)cos(x)

Next, we notice that both sides of the equation are multiplied by 2, so we can divide both sides by 2. This yields the equation:

cos(x) = sin(x)cos(x)

We can now divide both sides of the equation by cos(x), which leaves us with:

sin(x) = 1 

Finally, we must think about the angles at which sin(x) is equal to 1. You should realize, perhaps by imagining the unit circle, that sine is equal to 1 whenever x = π/2 + n2π, where n is any integer. 

However, this is not the final answer, as the problem gave us a restricted domain for x. x must be in between 0 and 3π. Therefore, the only possible values for x are π/2 and 5π/2.

So, the answer is:

x = π/2 and 5π/2

Sanveer R. IB Maths tutor, IB Economics tutor

7 months ago

Answered by Sanveer, an IB Maths tutor with MyTutor

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


£22 /hr

Guy P.

Degree: Mathematics (Masters) - Warwick University

Subjects offered:Maths, Further Mathematics + 2 more

Further Mathematics

“Hi there. Thank you for taking the time to visit my profile, it would be great to meet in a FREE 15-minute meeting! I look forward to hearing from you soon!”

£20 /hr

Ana S.

Degree: Physics (Bachelors) - Oxford, Balliol College University

Subjects offered:Maths, Physics+ 3 more

-Oxbridge Preparation-

“A friendly and understanding tutor with three years experience in school clubs, summer camps and private tutoring.”

£20 /hr

Ayokansola A.

Degree: Civil and Structural Engineering with a Year in Industry (Masters) - Sheffield University

Subjects offered:Maths, Spanish+ 4 more


“About Me: Hello! I am a Civil Engineering student at the University of Sheffield. I have always had a natural incline towards all things Maths and Science, so without a doubt, my genuine passion for the subjects’ I am offering will be...”

About the author

Sanveer R.

Currently unavailable: for regular students

Degree: Management (Bachelors) - LSE University

Subjects offered:Maths, Economics


“Who Am I: My name is Sanveer, but you can call me Sunny. I have Indian origins, but I grew up in Switzerland, where I lived for 14 years before moving to the UK. My passions include basketball and music. I am a student studying Manage...”

You may also like...

Other IB Maths questions

When do you use 'n choose k' and where does the formula come from?

A scalene triangle has base of 5cm. The angle opposite to the base is 63°, and a second angle is 72°. Find the area of the traingle

Talk about the relation between differentiability and continuity on a real function and its derivative.

Differentiate x^3 + y^4 = 34 using implicit differentiation

View IB 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