To find the value of tan θ, we start with the coordinates of point P, which are (3, 4). In trigonometry, the tangent of an angle is defined as the ratio of the opposite side to the adjacent side in a right triangle. In this case, we can consider the point P as part of a right triangle where:
- The opposite side (y) is 4
- The adjacent side (x) is 3
Now, we can use the formula for tangent:
tan θ = opposite / adjacent
Substituting the values we found:
tan θ = 4 / 3
Thus, the value of tan θ is 4/3. This means that for every 3 units along the x-axis, the height of the triangle rises by 4 units, reflecting the steepness of the angle in standard position corresponding to point P.