Question

Find the approximate values of : sin 61° , given that 1° = 0.0174^c, `sqrt(3) = 1.732`

Answer 1

Let f(x) = sin x

Then f'(x) = `d/dx(sin x) = cos x`

Take a = 60° = `pi/(3) and h = 1°` = 0.0174^c

Then f(a) = `f(pi/3)`

= `sin  pi/(3)`

= `sqrt(3)/(2)`

= `(1.732)/(2)`

= 0.866
and
f'(a) = `f'(pi/3)`

= `cos  pi/(3)`

= `(1)/(2)`
= 0.5
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)

∴ sin 61° = f(61°)

= `f(pi/3 + 0.0174)`

≑ `f(pi/3) + 0.0174.f'(pi/3)`

≑ 0.866 + 0.0174 x 0.5
≑ 0.866 + 0.00870
= 0.8747
∴ sin 61° ≑ 0.8747.