3.2 Use your calculator to insert the following function: $$ g(x)=1-2 \sin ^{2} x ; \quad x \in\left[-180^{\circ} ; 180^{\circ}\right] $$

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Below is one way to enter and view the function on a graphing calculator:

1. Make sure your calculator is set to degree mode (since x is given in degrees). For many calculators, you can do this by accessing the MODE menu and selecting “Degrees” instead of “Radians.”

2. Press the graph (or Y=) key to enter a new function.

3. Enter the function exactly as it appears. Because multiplication and the proper order of operations are important, use parentheses for sin x:
  1 – 2·(sin(x))²
  Some calculators require you to enter sin(x) and then use a squared function key, so the expression might be entered as:
  1 – 2·[ (sin(x))² ]
  Make sure you insert the parentheses properly so that only the sine is squared.

4. Set the window for x-values:
  Xmin = –180 and Xmax = 180.
  (Also adjust the Ymin and Ymax if needed for a clear view.)

5. Press the GRAPH button to display the function.

Note: You might recognize that the identity cos 2x = 1 – 2 sin²x means that your function is equivalent to g(x) = cos 2x. However, when using your calculator it is best to input the function as given unless instructed otherwise.

By following these steps, you should successfully graph g(x) = 1 – 2 sin²x over the domain [–180°, 180°].
To graph the function $$ g(x) = 1 - 2 \sin^2 x $$ on your calculator: 1. Set the calculator to degree mode. 2. Enter the function as $$ 1 - 2 	imes (\sin(x))^2 $$. 3. Set the x-range from –180° to 180°. 4. Press GRAPH to display the function.

3.2 Use your calculator to insert the following function: \( g(x)=1-2 \sin ^{2} x ; \quad x \in\left[-180^{\circ} ; 180^{\circ}\right] \)

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