Find an angle theta coterminal to -283^(@), where 0^(@) <= theta < 360^(@). Answer:

Find Coterminal Angle: To find a coterminal angle, we can add or subtract multiples of 360 degrees (a full circle) to the given angle until the result is within the specified range of 0 degrees to less than 360 degrees. Since -283 degrees is negative, we will add 360 degrees to find a positive coterminal angle.Add 360 Degrees: Add 360 degrees to -283 degrees to find a coterminal angle. theta = -283 degrees + 360 degrees theta = 77 degreesCheck Range: Check if the found angle is within the specified range. 0 degrees <= 77 degrees < 360 degrees This is true, so 77 degrees is a coterminal angle to -283 degrees within the specified range.

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Find an angle
theta coterminal to
-283^(@), where
0^(@) <= theta < 360^(@).
Answer:

Find an angle $\theta$ coterminal to $-283^{\circ}$ , where 0^{\circ} \leq \theta<360^{\circ} . $\newline$ Answer:

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Precalculus

Coterminal and reference angles

Full solution

Q. Find an angle

\theta

coterminal to

-283^{\circ}

, where

0^{\circ} \leq \theta<360^{\circ}

\newline

Answer:

Find Coterminal Angle: To find a coterminal angle, we can add or subtract multiples of $360$ degrees (a full circle) to the given angle until the result is within the specified range of $0$ degrees to less than $360$ degrees. Since $-283$ degrees is negative, we will add $360$ degrees to find a positive coterminal angle.
Add $360$ Degrees: Add $360$ degrees to $-283$ degrees to find a coterminal angle. $\newline$ $\theta = -283$ degrees $+ 360$ degrees $\newline$ $\theta = 77$ degrees
Check Range: Check if the found angle is within the specified range. $\newline$ 0^\circ \leq 77^\circ < 360^\circ $\newline$ This is true, so $77^\circ$ is a coterminal angle to $-283^\circ$ within the specified range.