帮我反推这两个公式,谢谢。

来源:百度知道 编辑:UC知道 时间:2024/06/01 10:01:11
已知如下,现在求反算A..B的公式
X=436+A×COS8°+B×SIN8°
Y=410+B×COS8°-A×SIN8°

G=(X-436) H=(Y-410)

G=Acos8°+Bsin8°

H=-Asin8°+Bcos8°

Gsin8°=Acos8°sin8°+Bsin^2 8°

Gcos8°=Acos^2 8°+Bcos8°sin8°

Hsin8°=-Asin^2 8°+Bcos8°sin8°

Hcos8°=-Asin8°cos8°+Bcos^2 8°

Gcos8°- Hsin8° = Acos^2 8°+Asin^2 8° = A

Gsin8°+ Hcos8° = Bsin^2 8°+Bcos^2 8° = B

A = (X-436)cos8°- (Y-410)sin8°

B = (X-436)sin8°+ (Y-410)cos8°

A = -(436×COS8°-X×COS8°-410×SIN8°+Y×SIN8°)/(COS²8° + SIN²8°)
B = -(410×COS8°-Y×COS8°+436×SIN8°-X×SIN8°)/(COS²8° + SIN²8°)

X=436+A×COS8°+B×SIN8°
Y=410+B×COS8°-A×SIN8°

X-436=A×COS8°+B×SIN8°(1)
Y-410=B×COS8°-A×SIN8° (2)
(1)式两边同时乘以COS8°,
得(X-436)×COS8°=A×COS8°^2+B×SIN8°×COS8°(3)
(2)式两边同时乘以SIN8°,
得(Y-410)×SIN8°=B×COS8°×SIN8°-A×SIN8°^2 (4)
(3)-(4)
得(X-436)×COS8°-(Y-410)×SIN8°=A×COS8°^2+A×SIN8°^2
所以
A=(X-436)×COS8°-(Y-410)×SIN8°
将A代入(1),

B=(X-436)×SIN8°+(