same circle, over and over again, with constant speed.

We close this subsection with two little exercises on trigonometry.

[**EXERCISES**]{}

[**3.3**]{}\
(a) A flagpole that has a circumference of $w$ inches is planted on level ground. You are standing $H$ feet away from the center of the base of the flagpole. You find that the line-of-sight from yourself to the top of the flagpole makes an angle of $\theta$ degrees with the ground. Your eyeballs are $h$ feet above the ground. Find an expression for the height of the flagpole above the ground.\
(b) Check your answer by noting that when $\theta =30^{\circ}$, $H =200$ and $h =5$, the height is about $120$ feet.\
(c) How much does your answer change if the circumference is doubled?\
[**3.4**]{}\
Recall that the addition formula for the sine function is $$\sin (\alpha + \beta )=\sin (\alpha ) \cos (\beta ) + 
\cos (\alpha ) \sin (\beta )
\label{eq:7add}$$ Suppose that the symbol $\theta$ stands for some fixed angle. List all of the angles $\theta +  \alpha$ for which the graph of the $\sin$ function looks exactly the same as it does at $\theta$. (Hint: a possible wrong answer would be $\theta + n 