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

Answer:

The value of the tangent is $-\frac{4}{5}$.

Step-by-step 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:

$\tan \theta = \frac{y_{A}-y_{O}}{x_{A}-x_{O}}$ (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:

$\tan \theta = \frac{y_{A}-y_{O}}{x_{A}-x_{O}}$

$\tan \theta = \frac{8-0}{-10-0}$

$\tan \theta = -\frac{4}{5}$