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hampton inn & suites binghamton vestal vestal - Malaeb

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 \sin \phi = rac{\sin heta}{n}

📌 We seek \(\cos \phi\). Using the identity \(\cos^2 \phi = 1 - \sin^2 \phi\):

📌 \cos^2 \phi = 1 - \left(rac{\sin heta}{n}

📌 ight)^2 = 1 - rac{\sin^2 heta}{n^2}

📌 \cos \phi = \sqrt{1 - rac{\sin^2 heta}{n^2}}

📌 Thus, the expression for \(\cos \phi\) is:

📌 oxed{\sqrt{1 - rac{\sin^2 heta}{n^2}}}

📌 An ichthyologist is modeling the movement of a fish in a 3D aquatic environment using vector dynamics. Suppose the fish's velocity vector is \(\mathbf{v} = egin{pmatrix} 2 \ -1 \ 3 \end{pmatrix}\) and the direction of the current is given by \(\mathbf{c} = egin{pmatrix} 1 \ 2 \ -1 \end{pmatrix}\). Find the component of the fishâs velocity perpendicular to the current direction.

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