Trigonometric Functions as Projections

The period of the cosine function

Remember there is no difference between the position of a point P on the unit circle for an angle \(\theta\) and the position for angle \(\theta + n \times 360^\circ\), where n is a positive or negative integer. And if point P is the same, then the projection onto the x-axis must also be the same. From this we can conclude:

The result of this is that, like the sine function, \(\cos(\theta)\) is a periodic function. The function repeats itself every 360 degrees, as shown in the interactive below.

Exercises

1. What is the domain of the cosine function? (That is, for \(y=\cos(\theta)\) what are the minimum and maximum values \(\theta\) can take?)
2. Calculate \(\cos(360\,000\,036^\circ)-\cos(-324^\circ)\).
3. For what values of \(\theta\) does \(\cos(\theta)\)
   1. reach its maximum value?
   2. reach its minimum value?
   3. intersect the horizontal axis?

Check your answers