Hello there. To solve this question, we'll have to remember some properties about the unit circle and trigonometric functions.
The unit circle is:
For any values in the circle, the x and y coordinates of the points are equal to the cosine and sine of the angle, respectively;
By definition, when x is equal to zero, sin(0) is 0, since the radius of the circle will be at the x-axis, in other words, there will be no height for the triangle formed.
By the same reason, cos(0) = 1, because it is the point where the circle touches x = 1.
To find the tangent, we can apply the formula:
[tex]\tan (\alpha)=\frac{\sin (\alpha)}{\cos (\alpha)}[/tex]And use the values we know
[tex]\tan (0)=\frac{\sin (0)}{\cos (0)}=\frac{0}{1}=0[/tex]The geometric interpretation for the tangent in the unit circle can be seen above, it touches the x-axis when the angle is zero, therefore it is also zero.
