Question

sin (31°)
given 1° = 0.0175',
cos 30º = 0.8660​

Answer 1

Given : 1° = 0.0175',   cos 30º = 0.8660​  

To Find : sin (31°)

Solution:

f(x + Δx)  = f(x)   + f'(x)Δx

x  = 30°

Δx  = 1°

f(x)  = Sinx

f'(x) = Cosx

f(30°)  = sin30° =  0.5

f'(30°) = cos 30º = 0.8660​  

Δx  = 1° = 0.0175

Sin(30° + 1°)  = Sin(30°)  + cos 30º  (1°)

=> Sin (31°)  = 0.5 + 0.8660(0.0175)

=> Sin (31°)  = 0.515155

Sin (31°)  = 0.515155

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