Question

NO LINKS!! If the given angle is in standard position, find two positive coterminal angles and two negative coterminal angles.​

Answer 1

Coterminal angles have a difference of 360° or its multiples.

To find the coterminal angle add to it 360° or (360n)°, where n is a positive or negative integer.

Part (a)

Given angle is 100°.

Its coterminal angles are:

• 100° + 360° = 460°, 100° + 720° = 820°, positive
• 100° - 360° = - 260°, 100° -720° = - 620°, negative

Part (b)

Given angle is 145°.

Its coterminal angles are:

• 145° + 360° = 505°, 145° + 720° = 865°,
• 145° - 360° = - 215°, 145° -720° = - 575°.

Part (c)

Given angle is - 10°.

Its coterminal angles are:

• -10° + 360° = 350°, -10° + 720° = 710°,
• -10° - 360° = - 370°, -10° -720° = - 730°.

Answer 2

(a) Positive: 460° and 820°

Negative: -260° and -620°

(b) Positive: 505° and 865°

Negative: -215° and -575°

(c) Positive: 350° and 710°

Negative: -370° and -730°

Explanation:

Coterminal angles: Angles that have the same initial side and the same terminal sides.

To find the coterminal angles of angle θ:

• θ ± 360n, if θ is measured in degrees.
• θ ± 2πn, if θ is measured in radians.

Part (a)

Given angle:

• θ = 100°

Positive angles:

⇒ 100° + 360° = 460°

⇒ 100° + 360° × 2 = 820°

Negative angles:

⇒ 100° - 360° = -260°

⇒ 100° - 360° × 2 = -620°

Part (b)

Given angle:

• θ = 145°

Positive angles:

⇒ 145° + 360° = 505°

⇒ 145° + 360° × 2 = 865°

Negative angles:

⇒ 145° - 360° = -215°

⇒ 145° - 360° × 2 = -575°

Part (c)

Given angle:

• θ = -10°

Positive angles:

⇒ -10° + 360° = 350°

⇒ -10° + 360° × 2 = 710°

Negative angles:

⇒ -10° - 360° = -370°

⇒ -10° - 360° × 2 = -730°