Find an angle thetaθ coterminal to minus, 349, degrees−349 ∘ , where 0, degrees, is less than or equal to, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ .

1. Break Down the Problem

To find an angle θ that is coterminal with -349 degrees, we first need to add or subtract multiples of 360 degrees until the resulting angle falls within the range of 0 degrees to 360 degrees.

2. Relevant Concepts

Coterminal angles differ by full rotations of 360 degrees. Therefore, we can find a coterminal angle by using the formula: $\theta = \text{original angle} + 360k$ where $k$ is an integer.

3. Analysis and Detail

1. Start with the original angle: $\theta = -349^\circ$
2. To find a positive coterminal angle, we can add 360 degrees: $\theta_{coterminal} = -349^\circ + 360^\circ = 11^\circ$

4. Verify and Summarize

The calculated coterminal angle is $11^\circ$. Since this angle is within the specified range of 0 degrees to 360 degrees, it is indeed the correct answer.

Final Answer

$\theta = 11^\circ$