Solution assignment 02 Unit circle and simple formulas

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Assignment 2

In which quadrant do the following angles (in radians) lie:

\displaystyle\frac{\pi}{6}    \displaystyle\frac{5\pi}{6}    \displaystyle\frac{5\pi}{3}    \displaystyle\frac{13\pi}{3}

Solution

According to the definition we have for an angle x:

x\in[0,\displaystyle\frac{\pi}{2}]\rightarrow{I}

x\in[\displaystyle\frac{\pi}{2},\pi]\rightarrow{II}

x\in[\pi,\displaystyle\frac{3\pi}{2}]\rightarrow{III}

x\in[\displaystyle\frac{3\pi}{2},2\pi]\rightarrow{IV}

For angles of x outside the interval [0,2\pi] we have to add or subtract 2\pi as many times as necessary until the angle lie in the given interval.

Thus:

\displaystyle\frac{\pi}{6}\rightarrow{I}

\displaystyle\frac{5\pi}{6}\rightarrow{II}

\displaystyle\frac{5\pi}{3}\rightarrow{III}

\displaystyle\frac{13\pi}{3}=4\displaystyle\frac{1}{3}\pi\rightarrow{4\displaystyle\frac{1}{3}\pi-2.2\pi}=\displaystyle\frac{1}{3}\pi\rightarrow{I}

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