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First published on Thursday, Jan 9, 2025 and last modified on Thursday, Jan 9, 2025
Mathedu
Polar Coordinates, Rotation
For the use of the test, we give you the table of the cosine and sine of some angles in Radian.
Denote \( \overrightarrow{u}_{1}\) that vector, and calculate successively:
The norm \( R_{1}\) of \( \overrightarrow{u}_{1}\) .
Use the formula \( \sqrt{p^{2}q}=p\sqrt{q}\) for \( p\) and \( q\) positive integers.
The cosine \( \cos(\theta_{1})\) of the polar angle of \( \overrightarrow{u}_{1}\) .
Simplify the fraction and use the formula \( \frac{p}{\sqrt{q}}=\frac{p\sqrt{q}}{q}\) for \( p\) and \( q\) positive integers.
The sine \( \sin(\theta_{1})\) of the polar angle of \( \overrightarrow{u}_{1}\) .
Simplify the fraction and use the formula \( \frac{p}{\sqrt{q}}=\frac{p\sqrt{q}}{q}\) for \( p\) and \( q\) positive integers.
The polar angle \( \theta_{1}\) of \( \overrightarrow{u}_{1}\) .
Use the table 1.
Denote \( \overrightarrow{u}_{2}\) that vector, and calculate successively:
The norm \( R_{2}\) of \( \overrightarrow{u}_{2}\) .
The cosine \( \cos(\theta_{2})\) of the polar angle of \( \overrightarrow{u}_{2}\) .
The sine \( \sin(\theta_{2})\) of the polar angle of \( \overrightarrow{u}_{2}\) .
The polar angle \( \theta_{2}\) of \( \overrightarrow{u}_{2}\) .
Use the table 1.