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\(\dfrac{13\pi}4\equiv\dfrac\pi4\mod2\pi\)

Or, put another way, since \(\dfrac{13\pi}4=2\pi+\dfrac\pi4\), it follows that \(\dfrac\pi4\) is an equivalent angle.

Answer:

Step-by-step explanation:

Given is an angle \(\frac{13\pi}{4}\)

We know that there are 2pi radians in each circle

Hence after crossing 2pi radians, the values repeat

\(\frac{13\pi}{4}=2\pi+\frac{5\pi}{4}\)

Hence equivalent angle is

\(\frac{5\pi}{4}\)

i.e. in the III quadrant making pi/4 with negative x axis.

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