Question

sin61°,Find approximate value.

Answer 1

we have to find approximate value of sin61°
using binomial expansion,
if y = (a ±b)ⁿ in such a way that y = aⁿ(1 + b/a)ⁿ
and 1 >>> b/a then, y ≈ aⁿ (1 + nb/a)

sin61° = sin(60 + 1)°

= sin60°.cos1° + cos60°.sin1°

if $\theta$ is very small then $sin\theta\approx\theta$ and $cos\theta\approx1$
here, 1° is very small. so, sin1° = sinπ/180 ≈ π/180
and cos1° ≈ 1

so, sin61° ≈ √3/2 × 1 + 1/2 × π/180
≈ 1.732/2 + 0.5 × 3.14/180
≈ 0.866 + 3.14/360
≈ 0.866 + 0.008722
≈ 0.8747222

hence, approximate value of sin61° ≈ 0.8747222

Answer 2

Dear Student:

For finding we will define x =60°

and Δx=-1°

and use,Δy=dy/dx*(Δx)

And,also Δy=f(x+Δx)-f(x)

See the attachment: