Determine the angle $ heta $ in degrees for which the point $ (cos( heta), sin( heta)) $ is closest to the point $ left(frac{1}{2}, -frac{sqrt{3}}{2}
ight) $ on the unit circle.

Answer 1

To find θ in degrees, we first find the angle whose coordinates on the unit circle are closest to (1/2, -√3/2). This point corresponds to the angle -60 degrees or 300 degrees.

The point (cos(θ), sin(θ)) that is closest must satisfy the equation:

$ \cos(\theta) = \frac{1}{2} \text{ and } \sin(\theta) = -\frac{\sqrt{3}}{2} $

Thus, the angle θ is:

$ \theta = 300° $

Answer 2

To find θ where (cos(θ), sin(θ)) is closest to (1/2, -√3/2), we use the fact this point corresponds to -60 degrees or 300 degrees. So:

$ heta = 300° $

Answer 3

Using the point (1/2, -√3/2) on the unit circle:

$ heta = 300° $

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