Part 4/5:
To visualize this, one can sketch the unit circle, noticing how these relationships are reflected geometrically. A triangle drawn at this angle will show the respective values for sine and cosine based on their positions relative to the axes.
Graphical Representation of Sine and Cosine
When plotted, the sine function demonstrates a smooth wave-like oscillation. As we shift the sine function left or right on a graph, we can visualize how ( \sin\left(\frac{\pi}{2} - \theta\right) ) correlates to ( \cos(\theta) ). The sine function reaches its maximum at ( \frac{\pi}{2} ) and subsequently returns to zero, prompting a shift in parameters.