For the rotation 645^(@), find the coterminal angle from 0^(@) <= theta < 360^(@), the quadrant, and the reference angle. The coterminal angle is ◻^(@), which lies in Quadrant ◻, with a reference angle of ◻^(@).

Subtract 360 degrees: To find the coterminal angle between 0 and 360 degrees, subtract 360 degrees from 645 degrees until the result is within the desired range. 645 - 360 = 285Check within range: Since 285 is between 0 and 360 degrees, this is the coterminal angle we're looking for. The coterminal angle is 285 degrees.Determine quadrant: To determine the quadrant, note that angles between 270 and 360 degrees lie in Quadrant IV. 285 degrees is in Quadrant IV.Calculate reference angle: The reference angle is the acute angle formed by the terminal side of the angle and the x-axis. For angles in Quadrant IV, subtract the angle from 360 degrees. 360 - 285 = 75

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For the rotation
645^(@), find the coterminal angle from
0^(@) <= theta < 360^(@), the quadrant, and the reference angle.
The coterminal angle is
◻^(@), which lies in Quadrant
◻, with a reference angle of
◻^(@).

For the rotation $645^{\circ}$ , find the coterminal angle from 0^{\circ} \leq \theta<360^{\circ} , the quadrant, and the reference angle. $\newline$ The coterminal angle is $\square^{\circ}$ , which lies in Quadrant $\square$ , with a reference angle of $\square^{\circ}$ .

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Algebra 1

Transformations of quadratic functions

Full solution

Q. For the rotation

645^{\circ}

, find the coterminal angle from

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

, the quadrant, and the reference angle.

\newline

The coterminal angle is

\square^{\circ}

, which lies in Quadrant

\square

, with a reference angle of

\square^{\circ}

Subtract $360$ degrees: To find the coterminal angle between $0$ and $360$ degrees, subtract $360$ degrees from $645$ degrees until the result is within the desired range. $\newline$ $645 - 360 = 285$
Check within range: Since $285$ is between $0$ and $360$ degrees, this is the coterminal angle we're looking for. $\newline$ The coterminal angle is $285$ degrees.
Determine quadrant: To determine the quadrant, note that angles between $270$ and $360$ degrees lie in Quadrant IV. $\newline$ $285$ degrees is in Quadrant IV.
Calculate reference angle: The reference angle is the acute angle formed by the terminal side of the angle and the x-axis. For angles in Quadrant IV, subtract the angle from $360$ degrees. $\newline$ $360 - 285 = 75$