Questions: Find a positive angle less than (2 pi) that is coterminal with the given angle. [ frac35 pi6 ] A positive angle less than (2 pi) that is coterminal with (frac35 pi6) is (square)

$Find a positive angle less than (2 pi) that is coterminal with the given angle. [ frac35 pi6 ] A positive angle less than (2 pi) that is coterminal with (frac35 pi6) is (square)$

Transcript text: Find a positive angle less than $2 \pi$ that is coterminal with the given angle. \[ \frac{35 \pi}{6} \] A positive angle less than $2 \pi$ that is coterminal with $\frac{35 \pi}{6}$ is $\square$

Solution

Solution Steps

Step 1: Determine the Given Angle

The given angle is $ \frac{35\pi}{6} $.

Step 2: Identify $2\pi$

We know that $2\pi$ is the full rotation in radians, which is approximately $6.283185307179586$.

Step 3: Calculate the Coterminal Angle

To find a positive angle less than $2\pi$ that is coterminal with $ \frac{35\pi}{6} $, we compute: \[ \text{coterminal angle} = \frac{35\pi}{6} \mod 2\pi \]

Step 4: Simplify the Coterminal Angle

After performing the modulus operation, we find that the coterminal angle is: \[ \text{coterminal angle} = 5.759586531581288 \] To express this in terms of $\pi$, we divide by $\pi$: \[ \text{coterminal angle in terms of } \pi = \frac{5.759586531581288}{\pi} \approx \frac{11}{6}\pi \]

Step 5: Final Result

Thus, the positive angle less than $2\pi$ that is coterminal with $ \frac{35\pi}{6} $ is: \[ \frac{11\pi}{6} \]