Question

question given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function. \\(\cos 90^{\circ}\\)

Explanation:

Step1: Recall Unit Circle Definition

On the unit circle, for an angle \( \theta \), the coordinates of the point where the terminal side intersects the unit circle are \( (\cos\theta, \sin\theta) \).

Step2: Determine Position for \( 90^\circ \)

For \( \theta = 90^\circ \) (or \( \frac{\pi}{2} \) radians), the terminal side lies along the positive \( y \)-axis. The point of intersection with the unit circle is \( (0, 1) \).

Step3: Identify Cosine Value

From the coordinates \( (\cos\theta, \sin\theta) \), when \( \theta = 90^\circ \), the \( x \)-coordinate (which is \( \cos\theta \)) is \( 0 \). So, \( \cos 90^\circ = 0 \).

Answer:

\( 0 \)