Finding the largest angle, beta? .:Resolved:.

[voidflux]

Hello everyone!!
I'm stuck on this question!
It says, In a small angle approximation, tan beta ~ sin beta, and ~ means is the order of magnitude of
Use your calculator to find the largest angle, beta, (in radians) for which the difference of sin beta - tan beta is less than 21.6% of the sin beta value. Any idea's?

Thanks for listening!

[TheManWhoCan]

I think this might be it:

sinx - tanx < 0.216sinx

Substituting t = tan(x/2):

2t/(1+t²) - 2t/(1-t²) < 0.432t/(1+t²)

If you solve that for t, you can get x. Can't be arsed personally but I hope that helps.

[voidflux]

thanks for the info!!

[voidflux]

Do u know how to solve this problem with some sort of ratio?
My professor said, When finding a percent difference, use the absolute value of the difference. Any other idea's?

[voidflux]

ahhh, i figured it out,
you have to do trial and error!

sin(.6050)-tan(.6050)
---------------------------
       sin(.6050)