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 t and the position for angle t + n × 360 degrees, 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:

cos(t )=cos(t + n × 360)

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

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Exercises

1. What is the domain of the cosine function? (That is, what are the minimum and maximum values t can take?)
2. Calculate cos(360 000 036°)-cos(-324°).
3. For what values of t does cos(t)
   1. reach its maximum value?
   2. reach its minimum value?
   3. intersect the t-axis?

Check your answers