Questions: Find a positive angle less than (2 pi) that is coterminal with the given angle. [ frac13 pi4 ] A positive angle less than (2 pi) that is coterminal with (frac13 pi4) is (square). (Simplify your answer. Type your answer in terms of (pi). Use integers or fractions for any numbers in the expression.)

$Find a positive angle less than (2 pi) that is coterminal with the given angle. [ frac13 pi4 ] A positive angle less than (2 pi) that is coterminal with (frac13 pi4) is (square). (Simplify your answer. Type your answer in terms of (pi). Use integers or fractions for any numbers in the expression.)$

Transcript text: Find a positive angle less than $2 \pi$ that is coterminal with the given angle. \[ \frac{13 \pi}{4} \] A positive angle less than $2 \pi$ that is coterminal with $\frac{13 \pi}{4}$ is $\square$. (Simplify your answer. Type your answer in terms of $\pi$. Use integers or fractions for any numbers in the expression.)

Solution

Solution Steps

Step 1: Understand Coterminal Angles

Coterminal angles are angles that have the same initial and terminal sides but differ by a multiple of $2\pi$. To find a coterminal angle less than $2\pi$, we subtract multiples of $2\pi$ from the given angle until the result is within the desired range.

Step 2: Subtract $2\pi$ from the Given Angle

The given angle is $\frac{13\pi}{4}$. We subtract $2\pi$ (which is equivalent to $\frac{8\pi}{4}$) from $\frac{13\pi}{4}$: \[ \frac{13\pi}{4} - \frac{8\pi}{4} = \frac{5\pi}{4} \]

Step 3: Verify the Result

Check if $\frac{5\pi}{4}$ is less than $2\pi$: \[ \frac{5\pi}{4} < 2\pi \] Since $\frac{5\pi}{4}$ is indeed less than $2\pi$, it is the desired coterminal angle.

Final Answer

$\boxed{\frac{5\pi}{4}}$

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