MYTUTOR SUBJECT ANSWERS

339 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

4 months ago

Answered by Sanveer, an IB Maths tutor with MyTutor


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

23 SUBJECT SPECIALISTS

£20 /hr

Oliver T.

Degree: Mathematics (Masters) - Edinburgh University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“Hello! I'm currently a 2nd year Mathematics student at the University of Edinburgh with a sturdy passion for all things Mathematics. Not only do I love Maths, I love teaching Maths and helping people with problems. In particular, I en...”

£22 /hr

Hanumanth Srikar K.

Degree: Maths and Economics (Bachelors) - LSE University

Subjects offered: Maths, German+ 3 more

Maths
German
Further Mathematics
Economics
Chemistry

“Hanumanth Srikar Karri - London School of Economics”

£24 /hr

Josh R.

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Maths, Further Mathematics

Maths
Further Mathematics

“I study Maths at Warwick, I hope to be able to teach your child to love Maths and how to achieve top exam grades. ”

About the author

£20 /hr

Sanveer R.

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

Why is (-1)*(-1)=1?

What are the key elements to include in your Math assignment?

Solve the equation 8^(x-1) = 6^(3x) . Express your answer in terms of ln 2 and ln3 .

What does differentiation actually mean?

View IB Maths tutors

Cookies:

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

mtw:mercury1:status:ok