Question

draw an angle with the given measure in standard position. determine if you are moving clockwise or counterclockwise, which quadrant the terminal side lies in, the reference angle, and a positive and negative coterminal angle.

1. ( 330^{circ} )

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

1. ( -210^{circ} )

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

1. ( 60^{circ} )

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

1. ( 135^{circ} )

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

Explanation:

Step1: Determine the direction for \( - 210^{\circ}\)

Negative angles are measured clockwise.

Step2: Find the quadrant for \( - 210^{\circ}\)

\(-210^{\circ}+360^{\circ} = 150^{\circ}\). Since \(90^{\circ}<150^{\circ}<180^{\circ}\), the terminal side lies in Quadrant II.

Step3: Calculate the reference angle for \( - 210^{\circ}\)

The reference angle \(\theta_{r}=180^{\circ}-150^{\circ}=30^{\circ}\)

Step4: Find coterminal angles for \( - 210^{\circ}\)

For a positive coterminal angle: \(-210^{\circ}+360^{\circ}=150^{\circ}\)
For a negative coterminal angle: \(-210^{\circ}-360^{\circ}=-570^{\circ}\)

Step5: Determine the direction for \(60^{\circ}\)

Positive angles are measured counterclockwise.

Step6: Find the quadrant for \(60^{\circ}\)

Since \(0^{\circ}<60^{\circ}<90^{\circ}\), the terminal side lies in Quadrant I.

Step7: Calculate the reference angle for \(60^{\circ}\)

The reference angle \(\theta_{r}=60^{\circ}\)

Step8: Find coterminal angles for \(60^{\circ}\)

For a positive coterminal angle: \(60^{\circ}+360^{\circ}=420^{\circ}\)
For a negative coterminal angle: \(60^{\circ}-360^{\circ}=-300^{\circ}\)

Step9: Determine the direction for \(135^{\circ}\)

Positive angles are measured counterclockwise.

Step10: Find the quadrant for \(135^{\circ}\)

Since \(90^{\circ}<135^{\circ}<180^{\circ}\), the terminal side lies in Quadrant II.

Step11: Calculate the reference angle for \(135^{\circ}\)

The reference angle \(\theta_{r}=180^{\circ}-135^{\circ}=45^{\circ}\)

Step12: Find coterminal angles for \(135^{\circ}\)

For a positive coterminal angle: \(135^{\circ}+360^{\circ}=495^{\circ}\)
For a negative coterminal angle: \(135^{\circ}-360^{\circ}=-225^{\circ}\)

Answer:

2.

• Circle one: clockwise
• Quadrant: II
• Reference Angle: \(30^{\circ}\)
• Coterminal Angles: \(150^{\circ}\), \(-570^{\circ}\)

3.

• Circle one: counterclockwise
• Quadrant: I
• Reference Angle: \(60^{\circ}\)
• Coterminal Angles: \(420^{\circ}\), \(-300^{\circ}\)

4.

• Circle one: counterclockwise
• Quadrant: II
• Reference Angle: \(45^{\circ}\)
• Coterminal Angles: \(495^{\circ}\), \(-225^{\circ}\)