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  
\[\beta = \theta - (\theta - \beta ) = tan^{-1} ( \frac{4}{3} )- sin^{-1} ( \frac{2.5}{5} )=23.13^o \]