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= -
So, all we have to do is enter the specified angle's value θ = -
into the formula above:
( cos(θ) ,sin(θ) )
= ( cos ( -
) , sin ( -
) )
= ( cos ( 2
-
) , sin ( 2
-
) )
= ( cos (
) , sin (
)
= ( -
,
)
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)