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composition of approximation

Can anyone point me in the right direction for this:
WP_20160924_14_17_57_Pro.jpg465.7KB
If

sin⁡(θ)≈θ−16θ3\sin(\theta) \approx \theta - \frac{1}{6}\theta^3

then

sin⁡(12θ)≈12θ−16(12θ)3\sin(\frac{1}{2}\theta) \approx \frac{1}{2}\theta - \frac{1}{6}(\frac{1}{2}\theta)^3

as θ↦12θ\theta \mapsto \frac{1}{2}\theta. Similar mapping for cosine.
(edited 7 years ago)
Original post by RDKGames

Using equals signs as I can't find the Latex for approximations.


≈\approx

:smile:
Original post by ghostwalker
≈\approx

:smile:


Oh what the hell! I tried that the other day and I got an error, checked the Latex page and it doesn't include that there so I gave up lol. Maybe used the wrong slash.
(edited 7 years ago)
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TSR George
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Original post by RDKGames
If

sin⁡(θ)≈θ−16θ3\sin(\theta) \approx \theta - \frac{1}{6}\theta^3

then

sin⁡(12θ)≈12θ−16(12θ)3\sin(\frac{1}{2}\theta) \approx \frac{1}{2}\theta - \frac{1}{6}(\frac{1}{2}\theta)^3

as θ↦12θ\theta \mapsto \frac{1}{2}\theta. Similar mapping for cosine.


Thank you! Got it after realising I needed to use the binomial expansion on the sec part :biggrin:

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