Trigonometric Functions as Projections

The cosine function

1. The range of cos(t) is [-1,1]. (This is the same as the range of the sine function.) The line projecting from P to the x-axis is always inside the unit circle, so the value of x and hence cos(t) must always lie between -1 and 1.
2. The cosine function is positive in quadrants 1 and 4 and negative in quadrants 2 and 3, as shown. Because we're projecting onto the x-axis, cosine will be positive where x is positive.

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