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.