Now try to design your own ‘trig table’ problem. Think about how much information you need to give. Do you want there to be only one way to complete the empty cells?

We have provided some blank tables: one for you to use as the problem table and one for you to fill in as a suggested solution. You can use the ‘Notes’ space to give any extra details such as a range of values of \(\theta\) or possible functions that could be used to complete the table.

Will you use only functions such as \(\sin \theta\) and \(\sec \theta\) or will you use variants such as \(- \sin \theta\)?

Will you restrict the range of values of \(\theta\)? Will you give information such as “\(\theta\) is acute”?

How will you make sure your table can be completed without using a calcuator?

You could use special values like \(\tfrac{\pi}{3}\), as we did in the first table.

You could use exact values that come from Pythagorean triples, as we did in the second table.

You could specify angles using inverse trigonometric functions, such as \(\theta = \arcsin \tfrac{4}{5}.\) How can you make sure these angles are consistent with the range of values you choose for \(\theta\)?