Answered

Complete the table below:

[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline
$\theta$ & $\cos \theta$ & $90^{\circ}-\theta$ & $\sin \left(90^{\circ}-\theta\right)$ \\
\hline
0 & & & \\
\hline
30 & & & \\
\hline
60 & & & \\
\hline
90 & & & \\
\hline
120 & & & \\
\hline
150 & & & \\
\hline
180 & & & \\
\hline
\end{tabular}
\][/tex]



Answer :

GinnyAnswer
Let's fill in the table step by step with the correct values for each column: [tex]\( \cos \theta \)[/tex] and [tex]\( \sin (90^\circ - \theta) \)[/tex].

### Step-by-Step Computation:

1. For [tex]\( \theta = 0^\circ \)[/tex]:
- [tex]\( \cos 0^\circ = 1.0 \)[/tex]
- [tex]\( 90^\circ - 0^\circ = 90^\circ \)[/tex]
- [tex]\( \sin 90^\circ = 1.0 \)[/tex]

2. For [tex]\( \theta = 30^\circ \)[/tex]:
- [tex]\( \cos 30^\circ \approx 0.866 \)[/tex]
- [tex]\( 90^\circ - 30^\circ = 60^\circ \)[/tex]
- [tex]\( \sin 60^\circ \approx 0.866 \)[/tex]

3. For [tex]\( \theta = 60^\circ \)[/tex]:
- [tex]\( \cos 60^\circ \approx 0.500 \)[/tex]
- [tex]\( 90^\circ - 60^\circ = 30^\circ \)[/tex]
- [tex]\( \sin 30^\circ \approx 0.500 \)[/tex]

4. For [tex]\( \theta = 90^\circ \)[/tex]:
- [tex]\( \cos 90^\circ \approx 0.0 \)[/tex]
- [tex]\( 90^\circ - 90^\circ = 0^\circ \)[/tex]
- [tex]\( \sin 0^\circ = 0.0 \)[/tex]

5. For [tex]\( \theta = 120^\circ \)[/tex]:
- [tex]\( \cos 120^\circ \approx -0.500 \)[/tex]
- [tex]\( 90^\circ - 120^\circ = -30^\circ \)[/tex]
- [tex]\( \sin -30^\circ \approx -0.500 \)[/tex]

6. For [tex]\( \theta = 150^\circ \)[/tex]:
- [tex]\( \cos 150^\circ \approx -0.866 \)[/tex]
- [tex]\( 90^\circ - 150^\circ = -60^\circ \)[/tex]
- [tex]\( \sin -60^\circ \approx -0.866 \)[/tex]

7. For [tex]\( \theta = 180^\circ \)[/tex]:
- [tex]\( \cos 180^\circ = -1.0 \)[/tex]
- [tex]\( 90^\circ - 180^\circ = -90^\circ \)[/tex]
- [tex]\( \sin -90^\circ = -1.0 \)[/tex]

### Completed Table:

[tex]\[ \begin{array}{|c|c|c|c|} \hline \theta & \cos \theta & 90^\circ - \theta & \sin (90^\circ - \theta) \\ \hline 0^\circ & 1.0 & 90^\circ & 1.0 \\ \hline 30^\circ & 0.866 & 60^\circ & 0.866 \\ \hline 60^\circ & 0.500 & 30^\circ & 0.500 \\ \hline 90^\circ & 0.0 & 0^\circ & 0.0 \\ \hline 120^\circ & -0.500 & -30^\circ & -0.500 \\ \hline 150^\circ & -0.866 & -60^\circ & -0.866 \\ \hline 180^\circ & -1.0 & -90^\circ & -1.0 \\ \hline \end{array} \][/tex]