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Find the terminal point t = -3 on the unit circle:

A) (-1, 0)
B) (0, -1)
C) (-3, 0)
D) (0, 3)

1 Answer

1 vote

Final answer:

Upon evaluating the given options for the terminal point corresponding to t = -3 radians on the unit circle, none of the options accurately depict a point on the unit circle for that angle. The terminal points on the unit circle should have coordinates where each is between -1 and 1, so the correct answer must be re-evaluated.

Step-by-step explanation:

The question asks to find the terminal point on the unit circle for t = -3. Since we're working with the unit circle, terminal points are confined to coordinates on the circle where the distance from the origin is 1 unit. Therefore, options that have coordinates with magnitudes other than 1 can be eliminated. This leaves us with options A and B.

The unit circle makes use of angles measured in radians, and traditionally, positive angles are measured counterclockwise from the positive x-axis, while negative angles are measured clockwise. So an angle of t = -3 radians would be equivalent to moving 3 radians clockwise from the positive x-axis. Considering the standard unit circle, we can see that neither (-1, 0) nor (0, 3) would correspond to -3 radians since these points represent 0 radians (pointing to the left on the x-axis) and $rac{3\pi}{2}$ radians (pointing up on the y-axis) respectively.

Therefore, both those options can be dismissed. To find the correct terminal point, we can visualize rotating -3 radians from the positive x-axis and stopping at the correct point on the circle, which should have both x and y coordinates between -1 and 1 (since the radius is 1). Unfortunately, with the given options, none of them exactly represent a point on the unit circle corresponding to t = -3 radians. Thus, the correct answer should be recalculated or revised.

User Chris Pacejo
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