Question

1. - 225°

circle one: clockwise counterclockwise
quadrant: _
reference angle: _
coterminal angles: _ _

1. 210°

circle one: clockwise counterclockwise
quadrant: _
reference angle: _
coterminal angles: _ _

1. - 315°

circle one: clockwise counterclockwise
quadrant: _
reference angle: _
coterminal angles: _ _

Explanation:

Step1: Determine the rotation direction

Negative angles rotate clockwise, positive angles rotate counter - clockwise.
For \(-45^{\circ}\): rotate clockwise.
For \(-225^{\circ}\): rotate clockwise.
For \(210^{\circ}\): rotate counter - clockwise.
For \(-315^{\circ}\): rotate clockwise.

Step2: Find the quadrant

• For \(-45^{\circ}\): \(0^{\circ}\gt - 45^{\circ}\gt - 90^{\circ}\), so it is in the fourth quadrant.
• For \(-225^{\circ}\): \(-270^{\circ}\lt - 225^{\circ}\lt - 180^{\circ}\), add \(360^{\circ}\) to get \(135^{\circ}\), which is in the second quadrant.
• For \(210^{\circ}\): \(180^{\circ}\lt210^{\circ}\lt270^{\circ}\), so it is in the third quadrant.
• For \(-315^{\circ}\): add \(360^{\circ}\) to get \(45^{\circ}\), which is in the first quadrant.

Step3: Calculate the reference angle

• For \(-45^{\circ}\): \(\vert - 45^{\circ}\vert=45^{\circ}\).
• For \(-225^{\circ}\): \(180^{\circ}-(-225^{\circ}-(-180^{\circ})) = 45^{\circ}\).
• For \(210^{\circ}\): \(210^{\circ}-180^{\circ}=30^{\circ}\).
• For \(-315^{\circ}\): \(\vert - 315^{\circ}+360^{\circ}\vert = 45^{\circ}\).

Step4: Find coterminal angles

Coterminal angles are found by adding or subtracting \(360^{\circ}\).

• For \(-45^{\circ}\): \(-45^{\circ}+360^{\circ}=315^{\circ}\), \(-45^{\circ}-360^{\circ}=-405^{\circ}\).
• For \(-225^{\circ}\): \(-225^{\circ}+360^{\circ}=135^{\circ}\), \(-225^{\circ}-360^{\circ}=-585^{\circ}\).
• For \(210^{\circ}\): \(210^{\circ}+360^{\circ}=570^{\circ}\), \(210^{\circ}-360^{\circ}=-150^{\circ}\).
• For \(-315^{\circ}\): \(-315^{\circ}+360^{\circ}=45^{\circ}\), \(-315^{\circ}-360^{\circ}=-675^{\circ}\).

Answer:

• For \(-45^{\circ}\): Circle one: clockwise; Quadrant: IV; Reference Angle: \(45^{\circ}\); Coterminal Angles: \(315^{\circ}\), \(-405^{\circ}\)
• For \(-225^{\circ}\): Circle one: clockwise; Quadrant: II; Reference Angle: \(45^{\circ}\); Coterminal Angles: \(135^{\circ}\), \(-585^{\circ}\)
• For \(210^{\circ}\): Circle one: counterclockwise; Quadrant: III; Reference Angle: \(30^{\circ}\); Coterminal Angles: \(570^{\circ}\), \(-150^{\circ}\)
• For \(-315^{\circ}\): Circle one: clockwise; Quadrant: I; Reference Angle: \(45^{\circ}\); Coterminal Angles: \(45^{\circ}\), \(-675^{\circ}\)