已知sin20.1度=0.3437，sin20.2度=0.3453，試估計sin20度10分?

sin20°6' = 20.1° = 0.3437 , sin20°12' = sin20.2° = 0.3453

sin 3(20°10') = sin (20°6' + 2(20°12'))
sin 3(20°10') = sin 20°6' cos 2(20°12') + cos 20°6' sin 2(20°12')
sin 3(20°10') = sin 20°6' (1 - 2sin²20°12') + cos 20°6' * 2sin 20°12' cos 20°12'
sin 3(20°10') = 0.3437 (1 - 2 * 0.3453²) + √(1 - 0.3437²) * 2 * 0.3453 √(1 - 0.3453²)
sin 3(20°10') = 0.870378719
3sin 20°10' - 4sin³20°10' = 0.870378719
令 x = sin 20°10' , 則 4x³ - 3x + 0.870378719 = 0
令 f(x) = 4x³ - 3x + 0.870378719 ,
則 f(0.3437) > 0 > f(0.3453) , (0.3437 + 0.3453)/2 = 0.3445 ,
f(0.3445) > 0 > f(0.3453) , (0.3445 + 0.3453)/2 = 0.3449 ,
f(0.3445) > 0 > f(0.3449) , (0.3445 + 0.3449)/2 = 0.3447 ,
f(0.3447) > 0 > f(0.3449) , (0.3447 + 0.3449)/2 = 0.3448 ,
f(0.3447) > 0 > f(0.3448) , (0.3447 + 0.3448)/2 = 0.34475 ,
f(0.34475) > 0 > f(0.3448)
0.34475 < x < 0.3448
故 sin 20°10' = 0.3448.