Question

Kayla claims that she can find an approximate value for sin 1o without using a machine to do any
computations. Explain or show how she can do this (Hint: if you choose to explain the process, please be very specific. If you choose to show how it is done, you can use your calculator to check your approximation).

Answer 1

using:
f(x)≈f(xo)+f′(xo)(x−xo) <-- should be in your text

1° = 1° - 0°
so let xo = 0, then x = 1

we have :
f(x) = sinx
f'(x) = cosx
since we are using Calculus on trig, our x must be in radians
1° = π/180
f(1°) = sin0 + cos(0)(π/180-0)
= 0 + (1)(π/180)
= π/180
= mmmhh, without a "machine for calculation" ??

anyway, π/180 = .017453292
and sin 1° = .017452406, not bad if I may say so!!!!
(error ≈ .000000886)