Question

question given the following unit circle, rotate green dot to the appropriate angle and then find the exact value of the function. \\(\tan 0^{\circ}\\)

Explanation:

Step1: Recall the definition of tangent on the unit circle

The tangent of an angle \( \theta \) in the unit circle is defined as \( \tan\theta=\frac{\sin\theta}{\cos\theta} \), where \( (\cos\theta, \sin\theta) \) are the coordinates of the point on the unit circle corresponding to angle \( \theta \).

Step2: Find the coordinates for \( \theta = 0^\circ \)

For \( \theta = 0^\circ \), the point on the unit circle is \( (1, 0) \). So, \( \cos(0^\circ)=1 \) and \( \sin(0^\circ)=0 \).

Step3: Calculate \( \tan(0^\circ) \)

Using the formula \( \tan\theta=\frac{\sin\theta}{\cos\theta} \), substitute \( \sin(0^\circ)=0 \) and \( \cos(0^\circ)=1 \):

$$ \tan(0^\circ)=\frac{\sin(0^\circ)}{\cos(0^\circ)}=\frac{0}{1}=0 $$

Answer:

0