X軸(じく)で回転(かいてん)する

回転(かいてん)した後(あと)の値(あたい)

$$ \left( \begin{array}{ccc} a{11} & a{12} & a{13} & a{14}\ a{21} & a{22} & a{23} & a{24}\ a{31} & a{32} & a{33} & a{34}\ a{41} & a{42} & a{43} & a{44}\ \end{array} \right) \left(\begin{array}{ccc} 1 & 0 & 0 & 0 \ 0 & \cos\theta & -\sin\theta & 0\ 0 & \sin\theta & \cos\theta & 0\ 0 & 0 & 0 & 1\ \end{array} \right) = \left( \begin{array}{ccc} a{11} & M{12} & M{13} & a{14}\ a{21} & M{22} & M{23} & a{24}\ a{31} & M{32} & M{33} & a{34}\ a{41} & M{42} & M{43} & a{44}\ \end{array} \right)

$$\ M{12} = a{12} \times \cos\theta + a{13} \times \sin\theta \ M{22} = a{22} \times \cos\theta + a{23} \times \sin\theta \ M{32} = a{32} \times \cos\theta + a{33} \times \sin\theta \ M{42} = a{42} \times \cos\theta + a{43} \times \sin\theta \

$$\ M{13} = a{12} \times -\sin\theta + a{23} \times \cos\theta \ M{23} = a{22} \times -\sin\theta + a{23} \times \cos\theta \ M{33} = a{32} \times -\sin\theta + a{33} \times \cos\theta \ M{43} = a{42} \times -\sin\theta + a{43} \times \cos\theta \