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# Which polar coordinates represent the same point as (4, −𝜋/2)? (Select all that apply.)?

Which polar coordinates represent the same point as (4, −𝜋/2)? (Select all that apply.)

(−4, −3𝜋/2)

(4, −9𝜋/2)

(4, 5𝜋/2)

(−4, −𝜋/2)

(4, 3𝜋/2)

(−4, 𝜋/2)

### 3 Answers

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a way to check the answer is

convert all answer to rectangular coordinates

(4, -pi/2 ) =      in cartesian coordinates is (0, -4)

remember

x = r(cos(x))

y = r(sin(x))

so

(4 , -pi/2)  = (4*cos(-pi/2) , 4* sin(-pi/2)) = (0,-4)

(-4, -3pi/2)  = (-4*cos( -3pi/2),  -4*sin(-3pi.2) = (0,-4)

(4, -9pi/2 ) = (4*cos(-9pi/2), 4*sin(-9pi/2) ) = (0,-4)

(4, 3pi/2 ) = (4*cos(3pi/2) , 4*sin(3pi/2) ) = (0,-4)

•  Which polar coordinates represent the same point as (4, −𝜋/2)?

(Select all that apply.)

(−4, −3𝜋/2)

(4, −9𝜋/2)                                 ✔

(4, 5𝜋/2)

(−4, −𝜋/2)

(4, 3𝜋/2)

(−4, 𝜋/2)

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