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percentage errors in degree and radian

Hello friends, I have a question regarding mechanics / statics.

If we have say, 20° and the radian equivalent, (20π/180) which is π/9. If I take out the percentage error in replacing the sine of 20 by the radian value, I get

(sin 20 - π/9) / (sin 20) which is approximately 2.06%. However, doing the exact same thing with tan the difference is 4.09%. Why is there a big difference in these values?
Original post by leosco1995
Hello friends, I have a question regarding mechanics / statics.

If we have say, 20° and the radian equivalent, (20π/180) which is π/9. If I take out the percentage error in replacing the sine of 20 by the radian value, I get

(sin 20 - π/9) / (sin 20) which is approximately 2.06%. However, doing the exact same thing with tan the difference is 4.09%. Why is there a big difference in these values?


I have absolutely no idea what you are doing.

sin⁡20∘=sin⁡π9\displaystyle \sin 20^{\circ} = \sin \frac{\pi}{9}

There is no error.
Reply 2
Avatar for leosco1995
leosco1995
OP
2
I'm not talking about the sine of the radian value.. I just meant the radian value on its own (weird, but the question asked for that). Sorry for any confusion.
Reply 3
Avatar for davros
davros
16
Original post by leosco1995
I'm not talking about the sine of the radian value.. I just meant the radian value on its own (weird, but the question asked for that). Sorry for any confusion.


What is the actual question that you have been asked to solve?
Original post by davros
What is the actual question that you have been asked to solve?


This.
Reply 5
Avatar for leosco1995
leosco1995
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2
Sorry for the late reply. The question asks this:

"What is the percent n error in replacing the sine of 20 by the value of the angle in radians? Repeat for the tangent of 20 and explain the qualitative difference in the two error percentages."
Reply 6
Avatar for alow
alow
19
Original post by leosco1995
Sorry for the late reply. The question asks this:

"What is the percent n error in replacing the sine of 20 by the value of the angle in radians? Repeat for the tangent of 20 and explain the qualitative difference in the two error percentages."


So it's aking for the percentage difference between sin⁡20\sin 20 and π9\frac{\pi }{9}

Look at the graphs of tanx and sinx and you can see the gradient of tanx increases faster than sinx for x=0 to x=pi/9, which means that the tanx curve is farther away from y=pi/9 than the sinx curve.
Reply 7
Avatar for Hasufel
Hasufel
16
allow has it spot on - (repped) -

look at the plots on this page (and these are only for small angle approx`ns) - and see even how these differ!

http://en.wikipedia.org/wiki/Small-angle_approximation
Reply 8
Avatar for leosco1995
leosco1995
OP
2
Interesting.. I didn't know about those approximations.

Thanks for the answers.
But actually it comes out to be ➖2. 06%.why did you have taken the ➕2. 06%?Plz answer me!

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