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