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:<math>\mathbf{q}_2 = \mathbf{q}_y = \sin(\alpha/2)\cos(\beta_y)</math>
:<math>\mathbf{q}_3 = \mathbf{q}_z = \sin(\alpha/2)\cos(\beta_z)</math>
where α is a simple rotation angle (the value in radians of the [[angle of rotation]]) and cos(β<sub>''x''</sub>), cos(β<sub>''y''</sub>) and cos(β<sub>''z''</sub>) are the "[[direction cosine]]s"
===Tait–Bryan angles===
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