Trigonometric Functions as Projections

The period of the cosine function

1. The domain of $\cos (\theta )$ is $(-\mathrm{\infty },+\mathrm{\infty })$.
2. $\cos (360000{036}^{\circ })-\cos (-{324}^{\circ })=0$.
3. 1. $\cos (\theta )$ is at a maximum when point P is at the right of the unit circle, i.e. at (1,0). This occurs when $\theta =0^{\circ }$. It also happens at $\theta =-{360}^{\circ }$, $\theta ={360}^{\circ }$, and any other value of $\theta$ that satisfies $\theta =n\times {360}^{\circ }$ for integer n.
   2. $\cos (\theta )$ is at a minimum when point P is at the left of the unit circle, i.e. at (-1,0). This occurs when $\theta ={180}^{\circ }$. It also happens at $\theta =-{180}^{\circ }$, and any other value of $\theta$ that satisfies $\theta =180+n\times {360}^{\circ }$ for integer n.
   3. $\cos (\theta )$ intersects the horizontal axis when point P is at either (0,1) or (0,-1). This occurs when $\theta ={90}^{\circ }$ and $\theta ={270}^{\circ }$. It also happens at $\theta =-{90}^{\circ }$, $\theta =-{270}^{\circ }$, and any other value of $\theta$ that satisfies $\theta =90+n\times {180}^{\circ }$ for integer n. Note that the graph of $cos(\theta )$ passes through the horizontal axis twice as frequently as it reaches a minimum or maximum.

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