Take a look at the diagram below.

Half circle divided into sectors

We’ve used inequalities involving \(\sin \theta\), \(\cos \theta\) and \(\tan \theta\) to divide the semicircle into sectors.

Each sector in the diagram is defined by a different inequality.

For example, one sector is defined by the angles \(\theta\) between \(0\) and \(\pi\) for which \(\cos \theta < \sin \theta < \tan \theta.\)

Another sector is defined by \(\cos \theta< \tan \theta < \sin \theta.\)

  • Can you work out which inequality has been used to define each sector?

  • Which is the biggest sector?

  • If you extended the diagram to make a complete circle, how many extra sectors would you need?