The given problem requires us to find the value of \(\theta\) when \(\tan \theta = 1\). To solve this, we must understand the meaning of the trigonometric function tangent and where it equals 1.
- The tangent of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the adjacent side. In terms of the unit circle, \(\tan \theta\) is the y-coordinate divided by the x-coordinate.
- We need to determine when this value is 1.
- \(\tan \theta = 1\) when both the y-coordinate and x-coordinate are equal. On the unit circle, this occurs at angle \(45^\circ\) (or its equivalents in other quadrants, which are not considered here since the options are in positive degrees).
- A key angle to remember is \(45^\circ\), where the sides of the triangle formed with the origin are equal, thus making \(\tan 45^\circ = \frac{\text{opposite}}{\text{adjacent}} = \frac{1}{1} = 1\).
Thus, the correct answer is \(\theta = 45^\circ\).
Therefore, the correct option is: 45°