Question

point a is on the following unit circle. what are the coordinates of point a? enter an exact value or round to the nearest hundredth.

Explanation:

Step1: Recall unit circle coordinates

For a point on the unit circle with angle \(\theta\), the coordinates are \((\cos\theta, \sin\theta)\). Here, \(\theta = \frac{\pi}{4}\).

Step2: Calculate \(\cos\frac{\pi}{4}\)

We know that \(\cos\frac{\pi}{4} = \frac{\sqrt{2}}{2} \approx 0.71\) (since \(\sqrt{2} \approx 1.414\), so \(\frac{1.414}{2} \approx 0.71\)).

Step3: Calculate \(\sin\frac{\pi}{4}\)

Similarly, \(\sin\frac{\pi}{4} = \frac{\sqrt{2}}{2} \approx 0.71\).

Answer:

\((\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2})\) or approximately \((0.71, 0.71)\)