Question

Let f( x)= sin(x) Let g(x)=cos(x) a) Sketch the graph of f^2 b) Sketch the graph of g^2 c) Sketch the graph of f^2+g^2

Answer 1

Given:
f(x) = sin(x)
g(x) = cos(x).

Note that because sin²x + cos²x = 1, the value for f²+g² should be equal to 1.
Create the table shown below.

x f² g² f² + g²
-------- ---------- ----------- ------------
-π 0 1 1
-0.8π 0.3455 0.6545 1
-0.6π 0.9045 0.0955 1
-0.4π 0.9045 0.0955 1
-0.2π 0.3455 0.6545 1
0 0 1 1
0.2π 0.3455 0.6545 1
0.4π 0.9045 0.0955 1
0.6π 0.9045 0.0955 1
0.8π 0.3455 0.6545 1
π 0 1 1

A sketch is shown in the figure below.