Question

Find the approximate values of : cos(60° 30°), given that 1° = 0.0175°, `sqrt(3) = 1.732`

Answer 1

Let f(x) = cos x

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

Take a = 60° = `pi/(3)` and

h = 30°

= `(1/2)°`

= `(1/2 xx 00175)°`

= 0.00875°

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

= `cos  pi/(3)`

= `(1)/(2)`
= 0.5
f'(a) = `f'(pi/3)`

= `-sin  pi/(3)`

= `-sqrt(3)/(2)`

= `-(1732)/(2)`
= – 0.866
The formula for approximation is
f(a + h) ≑ f(a) + h.f'(a)
∴ cos(60° 30°)
= f(60° 30°)
= `f(pi/3 + 0.00875)`

≑ `f(pi/3) + 0.00875.f'(pi/3)`

≑ 0.5 + (0.00875) (– 0.8660)
≑ 0.5 – 0.0075775
= 0.4924225
π cos(60° 30°) ≑ 0.4924.