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

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.

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

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.

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 question

(edited 2 years ago)

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.

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)

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.

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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