What is the value of tan(θ) if the terminal side of angle θ in standard position passes through the point (3, 4)?

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To find the value of tan(θ) when the terminal side of the angle in standard position passes through the point (3, 4), we can use the definitions of the sides in a right triangle formed by the x and y coordinates.

In the coordinate point (3, 4):

  • The x-coordinate is 3, which represents the length of the adjacent side of the triangle.
  • The y-coordinate is 4, which represents the length of the opposite side of the triangle.

We can calculate tangent (tan) using the formula:

tan(θ) = Opposite / Adjacent

Substituting the values:

tan(θ) = 4 / 3

Therefore, the value of tan(θ) is 4/3.

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