Question

determine the coordinates of the point on the unit circle corresponding to the given central angle. if necessary, round your results to the nearest hundredth.
215°
a. (-0.82, 0)
c. (-0.82, -0.57)
b. (-0.57, -0.82)
d. (1, -0.57)
please select the best answer from the choices provided
o a
o b
o c
o d

Explanation:

Step1: Recall unit - circle formula

For a point \((x,y)\) on the unit circle corresponding to an angle \(\theta\), \(x = \cos\theta\) and \(y=\sin\theta\). Here \(\theta = 215^{\circ}\).

Step2: Calculate the \(x\) - coordinate

\(x=\cos(215^{\circ})\). Since \(215^{\circ}=180^{\circ} + 35^{\circ}\), \(\cos(215^{\circ})=-\cos(35^{\circ})\approx - 0.82\).

Step3: Calculate the \(y\) - coordinate

\(y = \sin(215^{\circ})\). Since \(215^{\circ}=180^{\circ}+35^{\circ}\), \(\sin(215^{\circ})=-\sin(35^{\circ})\approx - 0.57\).

Answer:

C. \((-0.82,-0.57)\)