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Which point on the unit circle corresponds to −4π3?

(3√2,−12)

(-12,3√2)

(12,−3√2)

(-3√2,12)

1 Answer

5 votes

The point on the unit circle corresponds to −4π3 is (-1/2, 3√/2) .Therefore , (-1/2, 3√/2) is correct .

We are aware that any point's coordinate on the unit circle may be found using

( cos(θ) ,sin(θ) )

Considering that into the formula above:

θ= -
(4\pi )/(3)

So, all we have to do is enter the specified angle's value θ = -
(4\pi )/(3) into the formula above:

( cos(θ) ,sin(θ) )

= ( cos ( -
(4\pi )/(3) ) , sin ( -
(4\pi )/(3) ) )

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

= ( cos (
(2\pi )/(3) ) , sin (
(2\pi )/(3) )

= ( -
(1)/(2) ,
(√(3))/(2) )

Evaluating the options:

(1/2, −3√/2) is in the fourth quadrant, not the third.

(-3√/2, 1/2) is in the second quadrant, not the third.

(-1/2, 3√/2) has the correct sine but the wrong cosine (should be negative).

(3√/2, −1/2) has both the correct cosine and sine for the third quadrant and the angle of −4π/3.

Therefore, the point (3√/2, −1/2) corresponds to −4π/3 on the unit circle.

Question

Which point on the unit circle corresponds to −4π/3 ?

(1/2, −3√/2)

(-3√/2, 1/2)

(-1/2, 3√/2)

(3√/2, −1/2)

User Vinestro
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8.7k points

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