Question

If (-10,8) is a point on the terminal side f a angle 0 in standard position what is the value of tan0?

Answer 1

The value of the tangent is
`-(4)/(5)`.

Explanation:

Let be
`A(x,y) = (-10, 8)` on the terminal side of an angle in standard position and let be
`O(x,y)` the origin of the angle and the origin of the Cartesian plane. By definition of tangent, we make use of the following expression:

`\tan \theta = (y_(A)-y_(O))/(x_(A)-x_(O))` (1)

Where:

`x_(A), x_(O)` - x-Coordinates of point A and point O.

`y_(A), y_(O)` - y-Coordinates of point A and point O.

If we know that
`x_(A) = -10, x_(O) = 0`,
`y_(A) = 8` and
`y_(O) = 0`, then the value of the tangent is:

`\tan \theta = (y_(A)-y_(O))/(x_(A)-x_(O))`

`\tan \theta = (8-0)/(-10-0)`

`\tan \theta = -(4)/(5)`