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

2 months ago

Answered by Sanveer, an IB Maths tutor with MyTutor

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


£20 /hr

Jakub K.

Degree: Physics and Astronomy (Masters) - Durham University

Subjects offered: Maths, Physics


“About meHi! My name is Jakub and I'm studying Physics and Astronomy at Durham University. I have been interested in sciences for as long as I can remeber and I really enjoy sharing thatpassion with others, be it through tutoring or a...”

£22 /hr

Rudolfs T.

Degree: Physics with Theoretical Physics (Masters) - Manchester University

Subjects offered: Maths, Physics


“I am a theoretical physics student at the University of Manchester. Even though I'm only in my first year I've had a lot of interaction with science already. I have participated and obtained medals in the International Physics Olympia...”

£20 /hr

Robert S.

Degree: Engineering Mathematics (Bachelors) - Bristol University

Subjects offered: Maths, Computing


“About Me: I’m a fresher studying Engineering Mathematics at Bristol University. When I was younger, I was neither particularly interested or any good at maths. It was not until GCSE’s that my teacher motivated and inspired me to achie...”

MyTutor guarantee

About the author

£20 /hr

Sanveer R.

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

Take the square root of 2i

How do i solve simultaneous equation with more than two equations and two unknowns?

Find the coordinates that correspond to the maximum point of the following equation: y = −16x^2 + 160x - 256

Factorise z^3+1 into a linear and quadratic factor. Let y=(1+i√3)/2. Show that y is a cube root of -1. Show that y^2=y-1. Find the value of (1-y)^6.

View IB Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss