## Angle of Tangent to Circle With x Axis

We can find the angle between a tangent to a circle and the and an axis as the difference between two angles.

To find the angle between the
$x$
axis and the tangent to the circle in the diagram, draw a line from the origin to the centre of the circle, a line from the centre of the circle to the
$x$
axis, and a radius from the centre of the circle to the tangent.

From the diagram,
$\theta = tan^{-1} ( \frac{4}{3} )$
and
$\theta - \beta = sin^{-1} ( \frac{2.5}{5} )$
then
$\beta = \theta - (\theta - \beta ) = tan^{-1} ( \frac{4}{3} )- sin^{-1} ( \frac{2.5}{5} )=23.13^o$