Question

For the ordered pair, give three other ordered pairs with θ between −360° and 360° that name the same point.

(−3, 330°)

Answer 1

Three other ordered pairs with θ between −360° and 360° that name the same point as (−3, 330°) are (−3, 30°), (−3, 690°), and (−3, -30°).

Step-by-step explanation:

Given the ordered pair (−3, 330°), we can find three other ordered pairs that name the same point by adding or subtracting 360° from the given angle:

• (−3, 30°)
• (−3, 690°)
• (−3, -30°)

These three ordered pairs have angles between −360° and 360° and represent the same point as the given ordered pair.

Answer 2

Answer:
`(357^(0),330^(0))`,
`(-3^(0),-30^(0))`,
`(357^(0),-30^(0))`

Step-by-step explanation:

For a ordered pair
`(\alpha ,\beta )`,
`(\alpha -2n_(1)\pi ,\beta -2n_(2)\pi )` represents the same point in the cartesian plane where
`n_(1)` and
`n_(2)` are any integers.

Given point is
`(-3^(0),330^(0))`

Taking
`n_(1)=-1,n_(2)=0`,

`(357^(0),330^(0))`

Taking
`n_(1)=0,n_(2)=1`,

`(-3^(0),-30^(0))`

Taking
`n_(1)=-1,n_(2)=-1`,

`(357^(0),-30^(0))`