Graphing Sine and Cosine Functions
When you plot the sine function, you create a smooth wave that oscillates between -1 and 1. The sine value comes from the y-coordinate on the unit circle, creating a pattern that repeats every 2π units.
The period of sine is 2π, which means the pattern completes one full cycle over this interval. The amplitude is 1, representing the distance from the midline to the highest point of the wave. This creates a range of , while the domain extends infinitely.
The cosine function follows a similar wave pattern but starts at a different position. Unlike sine, cosine begins at its maximum value (1) when θ = 0. Cosine represents the x-coordinate on the unit circle, creating a wave that's shifted compared to sine.
Quick Tip: Remember that sine starts at 0 and reaches its peak at π/2, while cosine starts at its peak (1) and reaches 0 at π/2. This 90° phase difference is key to understanding their relationship!
Both sine and cosine have the same period (2π) and amplitude (1), giving them identical ranges of and infinite domains. The main difference is their starting positions on the coordinate plane.
