Question

given that \\( \cos \theta = 0 \\), find the coordinates of the point where the terminal side of \\( \theta \\) intersects the unit circle if \\( \theta \\) is an obtuse angle. (1 point)
\\( \bigcirc ( 0, - 1 ) \\)
\\( \bigcirc ( 0, 1 ) \\)
\\( \bigcirc ( - 1, 0 ) \\)
\\( \bigcirc ( 1, 0 ) \\)

Explanation:

Step1: Recall the unit - circle coordinates

For a unit circle \(x^{2}+y^{2}=1\), the coordinates of a point on the unit circle corresponding to an angle \(\theta\) are \((\cos\theta,\sin\theta)\). Given \(\cos\theta = 0\), so \(x = 0\).

Step2: Determine the value of \(\sin\theta\) for an obtuse angle

Since \(\theta\) is obtuse (\(90^{\circ}<\theta<180^{\circ}\)). We know that \(\sin\theta>0\) in the second quadrant (\(90^{\circ}<\theta<180^{\circ}\)). Using the identity \(x^{2}+y^{2}=1\) with \(x = 0\), we get \(y^{2}=1\), so \(y=\pm1\). Because \(\theta\) is obtuse, \(y = 1\).

Answer:

\((0,1)\)