sin1°+sin2°+sin3°+……+sin45°等于多少？
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解：由于sin1°+sin2°+sin3°+……+sin45°不符等差数列和等比数列的关系，但我们知道可以利用幂级数展开近似来表示sin(x)≈x-x³/6，所以
sin1°+sin2°+sin3°+……+sin45°
=sin(1°×π/180°)+sin(2°×π/180°)+sin(3°×π/180°)+……+sin(45°×π/180°)
≈(π/180)-(π/180)³/6+(π/90)-(π/90)³/6+(π/60)-(π/60)³/6+……+(π/4)-(π/4)³/6
=π/180+π/90+π/60+……+(π/4)-(π/180)³/6-(π/90)³/6-(π/60)³/6-……-(π/4)³/6
=π/180·(1+2+3+……+45)-(π/180)³/6·(1³+2³+3³+……+45³)
=π/180·(1+45)·45/2-(π/180)³/6·((1+45)·45/2)²
=23π/4-529π³/17280
=17.115
精确值，
sin1°+sin2°+sin3°+……+sin45°=17.1346
sin1°+sin2°+sin3°+……+sin45°
=sin(1°×π/180°)+sin(2°×π/180°)+sin(3°×π/180°)+……+sin(45°×π/180°)
≈(π/180)-(π/180)³/6+(π/90)-(π/90)³/6+(π/60)-(π/60)³/6+……+(π/4)-(π/4)³/6
=π/180+π/90+π/60+……+(π/4)-(π/180)³/6-(π/90)³/6-(π/60)³/6-……-(π/4)³/6
=π/180·(1+2+3+……+45)-(π/180)³/6·(1³+2³+3³+……+45³)
=π/180·(1+45)·45/2-(π/180)³/6·((1+45)·45/2)²
=23π/4-529π³/17280
=17.115
精确值，
sin1°+sin2°+sin3°+……+sin45°=17.1346
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