Trigonometric Functions as Projections

The period of the tangent function

At first glance you might think that the tangent function has a period of 360°, the same as the sine and cosine functions. But the tangent function repeats every 180°, so \[\tan(\theta)=\tan(\theta+n\times180^\circ),\quad n\in\mathbb(Z)\]

This means that we get two full cycles of the tangent function for each full cycle of sine or cosine. Use the applet to get a feel for this.

Exercises

1. What is the domain of the tangent function? (That is, what are the values of \(\theta\) for which \(\tan(\theta)\) is defined?)
2. Calculate \(\tan(360\,000\,036^\circ)-\tan(216^\circ)\).
3. For what values of \(\theta\) is
   1. \(\tan(\theta ) = 0\)?
   2. \(\tan(\theta ) = 1\)?
   3. \(\tan(\theta ) = -1\)?

Check your answers