[SOLVED] How to calculate integral of sqrt( 2 - 2cos(t) ) ?

**nunos** · February 1st 2010, 03:58 PM

I want to evaluate the integral of this, but I am having some difficulty simplyfing the expresion to integrate. $\sqrt{2 - 2\cos t} = \sqrt{2} \sqrt{1-\cos t}$ and I don't know what else to do...

Any help is appreciated.

Thanks.

**Krizalid** · February 1st 2010, 04:16 PM

$\cos t=1-2\sin ^{2}\frac{t}{2}.$

**nunos** · February 1st 2010, 04:45 PM

Originally Posted by Krizalid

$\cos t=1-2\sin ^{2}\frac{t}{2}.$

Thanks for your reply. That does work. But, may I ask how did you know that? Certainly there's a way do deduce that expression.

Thanks.

**Krizalid** · February 1st 2010, 04:47 PM

Of course, just consider the double angle formula for the cosine, then $\cos2t=1-2\sin^2t,$ then i just put $t\mapsto\frac t2.$

**nunos** · February 1st 2010, 05:09 PM

Originally Posted by Krizalid

Of course, just consider the double angle formula for the cosine, then $\cos2t=1-2\sin^2t,$ then i just put $t\mapsto\frac t2.$

I have never used that trigonometric identity before, but now am aware of it. Thanks for your help.

Cheers.

Thread: [SOLVED] How to calculate integral of sqrt( 2 - 2cos(t) ) ?

LinkBack

Thread Tools

Display

[SOLVED] How to calculate integral of sqrt( 2 - 2cos(t) ) ?

Similar Math Help Forum Discussions

[SOLVED] Calculate peak of Gaussian distribution from known integral

[SOLVED] Can't figure out integral with sqrt

Using geometry, calculate the volume of the solid under z = \sqrt{ 64 - x^{2} - y^{2}

Evaluate the integral of 2cos(lnt)dt

Integral of sin^3 (sqrt(x)) / (sqrt(x))

Search Tags