Preview Activity 2.3.1.
If we consider the unit circle with 16 labeled special points in Figure 2.3.1, start at \(t = 0\text{,}\) and traverse the circle counterclockwise, we may view the height, \(h\text{,}\) of the traversing point as a function of the angle, \(t\text{,}\) in radians. From there, we can plot the resulting \((t,h)\) ordered pairs and connect them to generate the circular function pictured in the following figure, which tracks the height of a point traversing the unit circle.
(a)
(b)
Complete the following table with the exact values of \(h\) that correspond to the stated inputs.
| \(t\) | \(0\) | \(\frac{\pi}{6}\) | \(\frac{\pi}{4}\) | \(\frac{\pi}{3}\) | \(\frac{\pi}{2}\) | \(\frac{2\pi}{3}\) | \(\frac{3\pi}{4}\) | \(\frac{5\pi}{6}\) | \(\pi\) |
| \(h\) | |||||||||
| \(t\) | \(\pi\) | \(\frac{7\pi}{6}\) | \(\frac{5\pi}{4}\) | \(\frac{4\pi}{3}\) | \(\frac{3\pi}{2}\) | \(\frac{5\pi}{3}\) | \(\frac{7\pi}{4}\) | \(\frac{11\pi}{6}\) | \(2\pi\) |
| \(h\) | |||||||||
