To find the exact value of tangent, θ, where θ is an angle in standard position and its terminal side passes through the point (1, 3), we can use the properties of right triangles.
Given that the terminal side passes through the point (1, 3), we can visualize a right triangle with a base of 1 unit and a height of 3 units.
Using the Pythagorean theorem, we can find the hypotenuse of the triangle: Hypotenuse=√12+32=√1+9=√10 Now, we can determine the exact value of the tangent of the angle, θ, which is given by the ratio of the opposite side (3) to the adjacent side (1) in the right triangle: tanθ=adjacent opposite=13=3 Therefore, the exact value of tangent, θ, in simplest radical form is tanθ=3.
