Given that cosθ=0 , find the coordinates of the point where the terminal side of θ intersects the unit circle, if θ is a reflex angle.(1 point) Responses (0,−1) left parenthesis 0 comma negative 1 right parenthesis (1,0) left parenthesis 1 comma 0 right parenthesis (−1,0) left parenthesis negative 1 comma 0 right parenthesis (0,1)

1 answer

Given that \(\cos \theta = 0\), it indicates that the angle \(\theta\) corresponds to points where the x-coordinate is zero when considering the unit circle, which is defined by the equation \(x^2 + y^2 = 1\).

In this case, the possible angles that satisfy \(\cos \theta = 0\) are \(\theta = 90^\circ\) (or \(\frac{\pi}{2}\) radians) and \(\theta = 270^\circ\) (or \(\frac{3\pi}{2}\) radians).

Since we are considering that \(\theta\) is a reflex angle, that means \(\theta\) is greater than \(180^\circ\). Therefore, \(\theta\) would be \(270^\circ\).

At \(270^\circ\):

  • The coordinates on the unit circle are \((0, -1)\).

Thus, the coordinates of the point where the terminal side of \(\theta\) intersects the unit circle, when \(\theta\) is a reflex angle, is \((0, -1)\).

The correct answer is \((0, -1)\).