Question

question given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function. \cos 270^{\circ}

Explanation:

Step1: Recall unit circle definition

On the unit circle, for an angle \(\theta\), \(\cos\theta\) is the \(x\)-coordinate of the point where the terminal side of \(\theta\) intersects the unit circle.

Step2: Determine the point for \(270^\circ\)

The angle \(270^\circ\) (or \(\frac{3\pi}{2}\) radians) has its terminal side along the negative \(y\)-axis. The point of intersection with the unit circle is \((0, - 1)\).

Step3: Find the cosine value

Since \(\cos\theta\) is the \(x\)-coordinate, for the point \((0,-1)\), the \(x\)-coordinate is \(0\). So, \(\cos270^\circ = 0\).

Answer:

0