Find an angle theta*θ* coterminal to 903, degrees903∘, where 0, degrees, is less than or equal to, theta, is less than, 360, degrees0∘≤*θ*<360∘.

To find an angle \(\theta\) that is coterminal with \(903^\circ\) and lies within the range \(0^\circ \leq \theta < 360^\circ\), you need to subtract multiples of \(360^\circ\) from \(903^\circ\) until the result falls within the desired range.

Start by subtracting \(360^\circ\) from \(903^\circ\):

\[
903^\circ - 360^\circ = 543^\circ
\]

Since \(543^\circ\) is still greater than \(360^\circ\), subtract another \(360^\circ\):

\[
543^\circ - 360^\circ = 183^\circ
\]

Now, \(183^\circ\) is within the range \(0^\circ \leq \theta < 360^\circ\).

Thus, the angle \(\theta = 183^\circ\) is coterminal with \(903^\circ\) and lies within the specified range.

Would you like more details or have any questions?

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Here are 8 related questions:

1. What is an angle coterminal with \(-45^\circ\) that lies within the range \(0^\circ \leq \theta < 360^\circ\)?
2. How do you find a positive coterminal angle for \(720^\circ\)?
3. What is the smallest positive angle coterminal with \(450^\circ\)?
4. How many angles are coterminal with \(183^\circ\) between \(0^\circ\) and \(1080^\circ\)?
5. What is the angle coterminal with \(1267^\circ\) within the range \(0^\circ \leq \theta < 360^\circ\)?
6. Can you find an angle coterminal with \(90^\circ\) that is negative?
7. How do you determine if two angles are coterminal?
8. What is the coterminal angle for \(1350^\circ\) in the range \(0^\circ \leq \theta < 360^\circ\)?

**Tip:** Coterminal angles differ by multiples of \(360^\circ\), so you can add or subtract \(360^\circ\) repeatedly to find an equivalent angle within a specific range.

Learn how to find a coterminal angle to 903° that lies within the range of 0° to 360°. This problem involves trigonometric concepts and coterminal angles, explaining the process of subtracting multiples of 360° to achieve the desired angle. Suitable for students in Grades 9-12.

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