Given [tex]\(\sec \theta = -7.3\)[/tex], we need to find [tex]\(\sin \left(\theta - \frac{\pi}{2} \right)\)[/tex].
First, recall that [tex]\(\sec \theta = \frac{1}{\cos \theta}\)[/tex]. This means we can express [tex]\(\cos \theta\)[/tex] in terms of [tex]\(\sec \theta\)[/tex]:
[tex]\[
\cos \theta = \frac{1}{\sec \theta} = \frac{1}{-7.3} \approx -0.136986301369863
\][/tex]
Next, we use the trigonometric identity for the sine of a shifted angle:
[tex]\[
\sin \left(\theta - \frac{\pi}{2} \right) = -\cos \theta
\][/tex]
Substitute [tex]\(\cos \theta\)[/tex] into the identity:
[tex]\[
\sin \left(\theta - \frac{\pi}{2} \right) = -(-0.136986301369863) = 0.136986301369863
\][/tex]
Thus, the value of [tex]\(\sin \left(\theta - \frac{\pi}{2} \right)\)[/tex] is approximately [tex]\(0.14\)[/tex]. Therefore, the correct answer is:
[tex]\[
0.14
\][/tex]
