Questions: Find an angle θ coterminal to 903°, where 0° ≤ θ<360°.

Transcript text: Find an angle $\theta$ coterminal to $903^{\circ}$, where $0^{\circ} \leq \theta<360^{\circ}$.

Solution

Step 1: Find the Coterminal Angle

To find an angle $ \theta $ that is coterminal with $ 903^{\circ} $, we can use the formula:

\[ \theta = 903^{\circ} \mod 360^{\circ} \]

Step 2: Calculate the Modulus

Calculating the modulus gives us:

\[ \theta = 903^{\circ} - 2 \times 360^{\circ} = 903^{\circ} - 720^{\circ} = 183^{\circ} \]

Step 3: Verify the Range

The resulting angle $ 183^{\circ} $ is within the required range of $ 0^{\circ} \leq \theta < 360^{\circ} $.

Thus, the coterminal angle is \$\boxed{183^{\circ}}\$.

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