How do I approximate #tan(0.01)#?

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Answer 1 · 2017-05-15T21:01:12

To approximate using differential or linear approximation see below.

Let #y = f(x) = tanx# and #a=0#

The #dy = f'(x) dx = sec^2x dx# and #dx = x-a = x-0 = 0.01-0 = 0.01#

The (linear) approximation at #0# is

#y = f(0) + dy = f(0)+f'(0)dx = f(0)+f'(0) (0.01)#

# = 0+1(0.01) = 0.01#

#tan(0.01) ~~ 0.01#.

(My calculator give #0.0100003333 . . . #, so it's a pretty good approximation.)