Find the angle given the coordinates on the unit circle
Answer 1
Chloe Evans
Given the coordinates (\(\frac{1}{2}\), \(\frac{\sqrt{3}}{2}\)) on the unit circle, find the corresponding angle in degrees.
The unit circle has a radius of 1. The coordinates \((x, y) \) on the unit circle can be represented as \((\cos \theta, \sin \theta)\).
So, we have:
\( \cos \theta = \frac{1}{2}\)
\( \sin \theta = \frac{\sqrt{3}}{2}\)
We need to find the angle \(\theta\) where both conditions hold true. Using the trigonometric values, we know:
\( \cos 60^\circ = \frac{1}{2}\)
\( \sin 60^\circ = \frac{\sqrt{3}}{2}\)
Thus, the angle is:
\( \theta = 60^\circ \)
Answer 2
James Taylor
Given the coordinates ((frac{1}{2}), (frac{sqrt{3}}{2})) on the unit circle, find the corresponding angle in degrees.
On the unit circle, the coordinates ((x, y)) represent ((cos heta, sin heta)).
Thus:
(cos heta = frac{1}{2})
(sin heta = frac{sqrt{3}}{2})
Considering standard trigonometric identities, we know:
(cos 60^circ = frac{1}{2})
(sin 60^circ = frac{sqrt{3}}{2})
Thus, ( heta = 60^circ ).
Answer 3
Abigail Nelson
Given the coordinates ((frac{1}{2}), (frac{sqrt{3}}{2})), find the angle.
(cos heta = frac{1}{2} )
(sin heta = frac{sqrt{3}}{2} )
( heta = 60^circ )
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