The Student Room Group

Small angles

What counts as a small angle when using the small angle approximations?
Reply 1
Depends on the accuracy, but 30 degrees (pi/6) has a relative error of ~ 5% (for sin). Tan(pi/6) has a relative error of ~10% and cos(pi/6) has a relative error of ~0.5%.
(edited 2 years ago)
Reply 2
Original post by mqb2766
Depends on the accuracy, but 30 degrees (pi/6) has a relative error of ~ 5% (for sin). Tan(pi/6) has a relative error of ~10% and cos(pi/6) has a relative error of ~0.5%.

I was asking about the answer because I was doing a question where I got 0.2 and -6.8 as the answer and I had to discard the -6.8 because it’s not small
Reply 3
Radians or degrees? Can you upload the questionn / working?

The small angle approximations are shown as dashed lines here
https://www.desmos.com/calculator/rbiyvnpf2n
as above, +/-0.5 rad (pi/6) is about the limit for any analysis.
(edited 2 years ago)
Original post by Bigflakes
What counts as a small angle when using the small angle approximations?

You use the small angle approximations when they say that the angle is ~~>=0 like tending to 0
Reply 5
Original post by mqb2766
Radians or degrees? Can you upload the questionn / working?

The small angle approximations are shown as dashed lines here
https://www.desmos.com/calculator/rbiyvnpf2n
as above, +/-0.5 rad (pi/6) is about the limit for any analysis.

This is the questionCD6F9464-D903-45A1-9DEB-331475FC5E69.jpeg
(edited 2 years ago)
Reply 6
Sure, from the graph in the previous post, look at the cos (and sin) approximation at -3.4 radians and think about whether its representative. Numericallly
cos(-3.4) = -0.97
small angle approximation = -4.8
Its not very good. The +/-0.5 rad (pi/6 or 30 degrees) is a reaonable rule of thumb for the approximations to be "decent", again as shown in the graph.
(edited 2 years ago)
Reply 7
Original post by mqb2766
Sure, from the graph in the previous post, look at the cos (and sin) approximation at -3.4 radians and think about whether its representative. Numericallly
cos(-3.4) = -0.97
small angle approximation = -4.8
Its not very good. The +/-0.5 rad (pi/6 or 30 degrees) is a reaonable rule of thumb for the approximations to be "decent", again as shown in the graph.

ok thanks

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