If θ is an angle in standard position and its terminal side passes through the point (6,5), find the exact value of \tan\thetatanθ.
To find the exact value of tanθ, we need to know the values of the coordinates (x, y) of the point where the terminal side of angle θ passes through.
In this case, we are given that the terminal side passes through the point (6, 5).
The tangent of θ is defined as the ratio of the y-coordinate to the x-coordinate of the point on the terminal side of the angle. Therefore, tanθ = y / x.
In this case, y = 5 and x = 6, so tanθ = 5 / 6.
Hence, the exact value of tanθ is 5 / 6.
To find the exact value of tan(θ), we need to determine the ratio of the y-coordinate to the x-coordinate of the point where the terminal side of the angle θ passes through.
Given that the terminal side of θ passes through the point (6, 5), we can use these coordinates to determine the values of the y and x coordinates.
The y-coordinate represents the vertical distance from the origin to the point (6, 5), which is 5.
The x-coordinate represents the horizontal distance from the origin to the point (6, 5), which is 6.
Now, we can find the value of tan(θ) by taking the ratio of the y-coordinate to the x-coordinate.
tan(θ) = y/x = 5/6
So, the exact value of tan(θ) is 5/6.