60

QI

210

QIII

30

450 -360 90

Quadrantal Angle

-40

QIV

360

2𝜋

57.3°

2𝜋

360

.017 radian

𝟓𝟎 ∙𝝅

𝟏𝟖𝟎 =

𝟓𝟎𝝅

𝟏𝟖𝟎=

𝟓𝝅

𝟏𝟖 −𝟏𝟐𝟎 ∙

𝝅

𝟏𝟖𝟎 =

−𝟏𝟐𝟎𝝅

𝟏𝟖𝟎=

−𝟐𝝅

𝟑 𝟐𝟕𝟎 ∙

𝝅

𝟏𝟖𝟎 =

𝟐𝟕𝟎𝝅

𝟏𝟖𝟎=

𝟑𝝅

𝟐

𝝅

𝟔∙

𝟏𝟖𝟎

𝝅 =

𝟏𝟖𝟎

𝟔= 𝟑𝟎

−2𝝅

𝟓∙

𝟏𝟖𝟎

𝝅 =

−𝟑𝟔𝟎

𝟓= −𝟕𝟐

1.7𝝅

𝟏∙

𝟏𝟖𝟎

𝝅 =

𝟑𝟎𝟔

𝟏= 𝟑𝟎𝟔

3.45

𝟏∙

𝟏𝟖𝟎

𝝅 =

𝟔𝟐𝟏

𝝅

197°𝟒𝟎′

7𝝅

𝟔∙

𝟏𝟖𝟎

𝝅 =

𝟏𝟐𝟔𝟎

𝟔= 𝟐𝟏𝟎

Positive measure: 240 + 360 = 600°

Negative measure: 240 - 360 = -120°

Positive measure: 𝟗𝝅

𝟒+ 𝟐𝝅 =

𝟏𝟕𝝅

𝟒

Negative measure: 𝟗𝝅

𝟒− 𝟐𝝅 =

𝝅

𝟒

𝝅

𝟒− 𝟐𝝅 =

−𝟕𝝅

𝟒

-285 terminates in QI.

pos: -285 + 360 = 75

300 -(-420) 720

300 -(-300) 600

300 -(-60) 360

300 -660 -360

Coterminal angles have differences that equal 360 or multiples of 360.

-120 -240 -360

-120 -(-80) -40

-120 -60 -180

−𝟓𝝅

𝟗

𝒏𝒐𝒕 𝒂 𝒎𝒖𝒍𝒕𝒊𝒑𝒍𝒆 𝒐𝒇 𝟐𝝅

Positive measure: −𝟓𝝅

𝟔+ 𝟐𝝅 =

𝟕𝝅

𝟔

−𝟒𝟐𝟎 ∙𝝅

𝟏𝟖𝟎 =

−𝟒𝟐𝟎𝝅

𝟏𝟖𝟎=

−𝟕𝝅

𝟑