MYTUTOR SUBJECT ANSWERS

1817 views

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)

to:

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

9 months ago

Answered by Sanveer, an IB Maths tutor with MyTutor


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

36 SUBJECT SPECIALISTS

£20 /hr

Isobel B.

Degree: Theoretical Physics (Masters) - University College London University

Subjects offered:Maths, Science+ 5 more

Maths
Science
Physics
Further Mathematics
Economics
Art
-Personal Statements-

“I am 20 years old and currently studying Theoretical Physics at UCL. I have a lot of experience tutoring and have a passion to help others learn.”

£20 /hr

Ayokansola A.

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

Subjects offered:Maths, Spanish+ 4 more

Maths
Spanish
Science
Physics
English
Economics

“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...”

£36 /hr

Adam D.

Degree: Economics and Management (Bachelors) - Bristol University

Subjects offered:Maths, Economics

Maths
Economics

“I am a second year undergraduate student at the University of Bristol, studying Economics and Management. I achieved A* in Economics and Maths A-levels and an A* at maths GCSE so would be very happy to help any students who are studyi...”

About the author

Sanveer R.

Currently unavailable: for regular students

Degree: Management (Bachelors) - LSE University

Subjects offered:Maths, Economics

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

Let f(x)=x^2-ax+a-1 and g(x)=x-5. The graphs of f and g intersect at one distinct point. Find the possible values of a.

Solve for x: log2(x^4) = log2(16)

Given 1/2 + 1 + 2 + 2^2 + ... + 2^10 = a*2^b + c, find the values of a,b,c.

Solve the equation (2 cos x) = (sin 2 x) , for 0 ≤ x ≤ 3π .

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

mtw:mercury1:status:ok