Math Is Fun Forum

Core2Student

Guest

Another Radian Question

Here's another question that I am stuck on. I'm not sure how you would find the radius.

O is the centre of a circle of radius r cm and angle AOB = θ = 2 radians.

Given that the shaded area (the area of the sector take away the area of (r²sinθ)/2 (in other words, the triangle part of the sector) equals 20cm².

Find the value of r.

Thank you very much in advance.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Another Radian Question

The area of the sector is

. You need to solve

for

.

Core2Student

Guest

Re: Another Radian Question

Do I need to substitute θ = 2 radians into the equation?

Because I get:

r²=40/(θ-sinθ)

And I don't know how to continue after that. o_O

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Another Radian Question

Of course. You are given θ = 2. Thus

Core2Student

Guest

Re: Another Radian Question

Hmm, using what you posted, I got an answer of 4.51cm, whereas the answer in the book is 6.06cm. Perhaps there is a slip up somewhere?

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Another Radian Question

The angles are in radians. Switch your calculator to radians.

Core2Student

Guest

Re: Another Radian Question

Oh yeah. OMG. >_< I am so silly, I got all the way down to the r² bit fine, I just forgot that they were in radians. Oh dear. I need to make sure not to make the same mistake again.

Thank you.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Another Radian Question

You’re welcome. The most important thing is that you now understood the whole question.

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Another Radian Question

Easy mistake to make. You'll stop making it (as much) as you continue to do more maths (mainly because you work in radians pretty much the whole time).