Trigonometric Functions as Projections
The sine function
- The range of \(\sin(\theta)\) is [-1,1]. (That is, it can take
values from -1 to 1. The square brackets indicate that the range
includes both end values.) This should be easy to see from the
applet. The line projecting from P to the y-axis is
always inside the unit circle, so the value of y and hence
sin(t) must always lie between -1 and 1.
The sine function is positive in quadrants 1 and 2 and negative in
quadrants 3 and 4, as shown. Because we're projecting onto the
y-axis, sine will be positive where y is positive.