Find an angle theta coterminal to 902^(@), where 0^(@) <= theta < 360^(@). Answer:

Understand coterminal angles: Understand what a coterminal angle is. A coterminal angle to a given angle is an angle that differs from the given angle by a multiple of 360°. This is because adding or subtracting 360° from an angle does not change its position in the standard position on a coordinate plane.Calculate coterminal angle: Calculate the coterminal angle. Since 902° is more than 360°, we can subtract 360° multiples from it until we get an angle that is between 0° and 360°. We start by subtracting 360° once: 902° - 360° = 542°. This is still greater than 360°, so we subtract 360° again: 542° - 360° = 182°. This is still greater than 360°, so we subtract 360° one more time: 182° - 360° = -178°. Since we are looking for a positive angle, we add 360° to get a positive coterminal angle: -178° + 360° = 182°.

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

Find an angle $\theta$ coterminal to $902^{\circ}$ , where 0^{\circ} \leq \theta<360^{\circ} . $\newline$ Answer:

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Algebra 2

Find trigonometric ratios using reference angles

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Q. Find an angle

\theta

coterminal to

902^{\circ}

, where

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

\newline

Answer:

Understand coterminal angles: Understand what a coterminal angle is. $\newline$ A coterminal angle to a given angle is an angle that differs from the given angle by a multiple of $360°$ . This is because adding or subtracting $360°$ from an angle does not change its position in the standard position on a coordinate plane.
Calculate coterminal angle: Calculate the coterminal angle. $\newline$ Since $902^\circ$ is more than $360^\circ$ , we can subtract $360^\circ$ multiples from it until we get an angle that is between $0^\circ$ and $360^\circ$ . We start by subtracting $360^\circ$ once: $902^\circ - 360^\circ = 542^\circ$ . This is still greater than $360^\circ$ , so we subtract $360^\circ$ again: $542^\circ - 360^\circ = 182^\circ$ . This is still greater than $360^\circ$ , so we subtract $360^\circ$ one more time: $360^\circ$ $2$ . Since we are looking for a positive angle, we add $360^\circ$ to get a positive coterminal angle: $360^\circ$ $4$ .