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.)
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Solution

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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 2π2\pi. To find a coterminal angle less than 2π2\pi, we subtract multiples of 2π2\pi from the given angle until the result is within the desired range.

Step 2: Subtract 2π2\pi from the Given Angle

The given angle is 13π4\frac{13\pi}{4}. We subtract 2π2\pi (which is equivalent to 8π4\frac{8\pi}{4}) from 13π4\frac{13\pi}{4}: 13π48π4=5π4 \frac{13\pi}{4} - \frac{8\pi}{4} = \frac{5\pi}{4}

Step 3: Verify the Result

Check if 5π4\frac{5\pi}{4} is less than 2π2\pi: 5π4<2π \frac{5\pi}{4} < 2\pi Since 5π4\frac{5\pi}{4} is indeed less than 2π2\pi, it is the desired coterminal angle.

Final Answer

5π4\boxed{\frac{5\pi}{4}}

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