Computers either have an integer processing unit and/or a basic floating point unit. Using series expansions must take a lot of time if high accuracy is required. So how is say, tan(34.5) calculated so fast?
In: Engineering
Simple answer. Because the computer or calculator is running really fast.
A simple floating point operation or integer can be done in one clock cycle. And there are dedicated hardware to do special functions, but let’s ignore those for now.
With high end calculators running 10mhz processors that means they can do 10 million calculations per second. So yeah that’s basically instantaneous to you.
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