The diagram shows a circle with centre O. The radius of the circle is 18 cm and angle AOC is θ. Find the area of the shaded region ACB, giving your answer in terms of θ.

The circle has its center at $O$ and a radius of $r = 18$ cm.
The angle $\angle AOC$ is given as $\theta$.
The line segment $AB$ is tangent to the circle at point $A$, which means $\angle OAB = 90^\circ$.
Point $C$ lies on the line segment $OB$ and also on the circle. Therefore, $OC$ is a radius, and the angle $\angle AOB$ is equal to $\angle AOC$, which is $\theta$.

In $\triangle OAB$, $OA = r = 18$ cm.
Since $\angle OAB = 90^\circ$, we can use trigonometry to find the length of $AB$.

The area of $\triangle OAB$ is given by:

The area of a sector with radius $r$ and angle $\theta$ (in radians) is given by the formula $\frac{1}{2}r^2\theta$.

The shaded region $ACB$ is the area of $\triangle OAB$ minus the area of sector $OAC$.