# Thread: Finding the Linear Speed

1. ## Finding the Linear Speed

I just started college trig, I've been looking threw the book but can't find the method to this problem,
An object is traveling around a circle with a radius of 10 centimeters. If in 20 seconds a central angle of 1/3 radian is swept out, what is the linear speed of the object?
+8 cookies for who ever tells me what to do.

2. ## Re: Finding the Linear Speed

Also, if anyone knows a good place to help me with Trig Identities. I can remember all the identities, I just suck at seeing what to convert them into.
Just a site for tips and such is what I'm looking for. Thanks.

3. ## Re: Finding the Linear Speed

So it travels 1/3 of a radian in 20 seconds?

If so its travelling at (1/3)/20 = 1/60 radians per second or one radian per minute.

Trig identities can be found here: Table of Trigonometric Identities

4. ## Re: Finding the Linear Speed

In case I haven't asked enough already... :P

Use Fundamental Trig Identities/ Complementary Angle Theorem to find
If tan^2(theta) = 5, find the exact value of sec^2(theta).
I tried just makeing a triangle, with sides opposite = 1 and adjacent = 5, giving a hypotenuse of Sqrt26, so Sec would be... sqrt26/5...?

5. ## Re: Finding the Linear Speed

My final answer was 1/6 centimeters/minute... And yet I didn't get that good feeling you get from confidently answering a question...?
Thanks.

EDIT: I should have left it at 1/6 centimeters/SECOND, that makes much more sense...

6. ## Re: Finding the Linear Speed

$\displaystyle \tan^2\theta = 5$

And

$\displaystyle 1+\tan^2\theta = \sec^2\theta$

so $\displaystyle \sec^2\theta = \dots$

7. ## Re: Finding the Linear Speed

Originally Posted by Muzik
+8 cookies for who ever tells me what to do.
What type of cookies?

8. ## Re: Finding the Linear Speed

Dear pickslides,

Since 1 radian implies the arc length = radius = 10 cm., can't we say 10 cm. in one minute as the linear speed? I am not clear. Kindly enlighten me. Thanks.

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### an object is traveling around a circle with a radius of 20 meters. if in 10 seconds a central angle of 1/5 radian

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