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# percentage errors in degree and radian watch

1. 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?
2. (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.

There is no error.
3. 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.
4. (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?
5. (Original post by davros)
What is the actual question that you have been asked to solve?
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."
7. (Original post by leosco1995)

"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 and

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.
8. 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
9. Interesting.. I didn't know about those approximations.

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