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:

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

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

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

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

Return to Assignments Unit circle and simple formulas

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Solution assignment 02 Unit circle and simple formulas

Assignment 2

Solution

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