Using your calculator insert the following function g(x)=1-2 sin²x 2.2.1 Complete

Physics
1

Using your calculator insert the following function g(x)=1-2 sin²x 2.2.1 Complete the following table:

\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline x & -180° & -135° & -90° & -45° & 0° & 45° & 90° & 135° & 180° \ \hline 1-2 sin² x & & & & & & & & & \ \hline \end{tabular}

2

Completing the Function Table for ( g(x) = 1 - 2 \sin^2 x )

To complete the table for the given function g(x) = 1 - 2 \sin^2 x, we need to calculate the value of ( 1 - 2 \sin^2 x ) for each angle ( x ) in degrees. This function is based on the trigonometric identity for the sine function. Let’s calculate each value step-by-step for the given angles.

Key Steps:

  1. Find (\sin(x)): Determine the sine value for each angle.
  2. Calculate (\sin^2(x)): Square the sine value.
  3. Compute (g(x) = 1 - 2 \sin^2(x)): Insert the squared sine value into the expression and solve.

Calculate Each Value:

  1. For x = -180^\circ :
\sin(-180^\circ) = \sin(180^\circ) = 0
\sin^2(-180^\circ) = 0^2 = 0
1 - 2 \times 0 = 1
  1. For x = -135^\circ :
\sin(-135^\circ) = -\sin(135^\circ) = -\frac{\sqrt{2}}{2}
\sin^2(-135^\circ) = \left(-\frac{\sqrt{2}}{2}\right)^2 = \frac{2}{4} = \frac{1}{2}
1 - 2 \times \frac{1}{2} = 1 - 1 = 0
  1. For x = -90^\circ :
\sin(-90^\circ) = -\sin(90^\circ) = -1
\sin^2(-90^\circ) = (-1)^2 = 1
1 - 2 \times 1 = 1 - 2 = -1
  1. For x = -45^\circ :
\sin(-45^\circ) = -\sin(45^\circ) = -\frac{\sqrt{2}}{2}
\sin^2(-45^\circ) = \left(-\frac{\sqrt{2}}{2}\right)^2 = \frac{1}{2}
1 - 2 \times \frac{1}{2} = 1 - 1 = 0
  1. For x = 0^\circ :
\sin(0^\circ) = 0
\sin^2(0^\circ) = 0^2 = 0
1 - 2 \times 0 = 1
  1. For x = 45^\circ :
\sin(45^\circ) = \frac{\sqrt{2}}{2}
\sin^2(45^\circ) = \left(\frac{\sqrt{2}}{2}\right)^2 = \frac{1}{2}
1 - 2 \times \frac{1}{2} = 1 - 1 = 0
  1. For x = 90^\circ :
\sin(90^\circ) = 1
\sin^2(90^\circ) = 1^2 = 1
1 - 2 \times 1 = 1 - 2 = -1
  1. For x = 135^\circ
\sin(135^\circ) = \frac{\sqrt{2}}{2}
\sin^2(135^\circ) = \left(\frac{\sqrt{2}}{2}\right)^2 = \frac{1}{2}
1 - 2 \times \frac{1}{2} = 1 - 1 = 0
  1. For x = 180^\circ :
\sin(180^\circ) = 0
\sin^2(180^\circ) = 0^2 = 0
1 - 2 \times 0 = 1

Completed Table:

\begin{array}{|c|c|c|c|c|c|c|c|c|c|} \hline x & -180^\circ & -135^\circ & -90^\circ & -45^\circ & 0^\circ & 45^\circ & 90^\circ & 135^\circ & 180^\circ \\ \hline 1 - 2 \sin^2 x & 1 & 0 & -1 & 0 & 1 & 0 & -1 & 0 & 1 \\ \hline \end{array}

This table summarizes the output of the function g(x) = 1 - 2 \sin^2 x for the specified angles. Let me know if you have any further questions or need additional explanations!

@anonymous10

1 Like