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Thank you.

Stephen

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In summary, there are various ways to find the sin or cos of an angle without using a calculator. These include using double/triple angle identities, power series, and mental math tricks such as using exact sine ratios of angles to create linear approximations. However, the accuracy of these methods may vary and it ultimately depends on the level of accuracy needed for the specific angle.

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Thank you.

Stephen

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- #2

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You could also do a power series and add up the first few terms, I guess...

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Any help would be appreciated.

Stephen

- #4

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For

For example, it gives sin30º = 0.4997 and cos30º = 0.8661.

Is that close enough?

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StephenDoty said:

Any help would be appreciated.

Stephen

Double and triple identities don't require a calculator, neither does doing an infinite series if the angle is small enough...

- #6

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After that, either use sin or cos (30 degrees +/- x) expansions to reduce the problem to the sin/cos of an angle less than 20ish degrees, then use sin/cos (15 degrees +/- x) expansions to make the problem angle even smaller. At this point, everything else is still exact, now just approximate your small angle with the power series.

If you don't need it too exact, just a few d.p's, then Remember exact sine ratios of angles 0, 15, 30, 45, 60, 75, 90 degrees and use create a linear approximation from the one closest required angle.

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