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.)
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 2π. To find a coterminal angle less than 2π, we subtract multiples of 2π from the given angle until the result is within the desired range.
Step 2: Subtract 2π from the Given Angle
The given angle is 413π. We subtract 2π (which is equivalent to 48π) from 413π:
413π−48π=45π
Step 3: Verify the Result
Check if 45π is less than 2π:
45π<2π
Since 45π is indeed less than 2π, it is the desired coterminal angle.