Compare the graphs

f(è)=sinè and f(è)=sin(-è).
f(è)=cosè and f(è)=cos(-è).

What conclusions can you make?

e = theta :(

sine is an odd function.

cosine is an even function.

Look at the symmetry around Theta=0

To compare the graphs of the given functions, f(è) = sin(è) and f(è) = sin(-è), we need to understand the properties of the sine function.

1. Graphs of f(è) = sin(è) and f(è) = sin(-è):
The graph of f(è) = sin(è) is a periodic function that oscillates between -1 and 1 as the angle (è) varies. The graph starts at the origin (0, 0) and repeats itself every 360 degrees or 2π radians.

The graph of f(è) = sin(-è) is also a periodic function that oscillates between -1 and 1. However, in this case, the negative sign before è (inside the function) reflects the graph across the y-axis. Hence, the graph of f(è) = sin(-è) is symmetric with respect to the y-axis.

2. Observations:
Comparing f(è) = sin(è) and f(è) = sin(-è), we can conclude that these functions are not the same. The reflection across the y-axis in f(è) = sin(-è) changes the orientation of the graph compared to f(è) = sin(è). The two graphs will have the same shape but will start at different points and move in opposite directions.

Similarly, we can compare f(è) = cos(è) and f(è) = cos(-è). The cosine function also oscillates between -1 and 1, but it has a different starting point and shape compared to the sine function.

Thus, the conclusions we can make are:
- The graphs of f(è) = sin(è) and f(è) = sin(-è) are reflections of each other across the y-axis.
- The graphs of f(è) = cos(è) and f(è) = cos(-è) are the same because the cosine function is an even function, meaning it is symmetric with respect to the y-axis.