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