Answer:
D
Step-by-step explanation:
Recall that:
[tex]\displaystyle \cos\theta = \frac{1}{\sec\theta}[/tex]
Since we are given that secθ = -7.3, then by definition:
[tex]\displaystyle \cos\theta = \frac{1}{(-7.3)}\approx -0.14[/tex]
Next, recall that:
[tex]\displaystyle \sin\left (\frac{\pi}{2} - \theta \right) = \cos\theta[/tex]
This is the co-function identity.
And since sine is an odd function:
[tex]\sin u = -\sin (-u)[/tex]
In other words:
[tex]\displaystyle \sin\left (\frac{\pi}{2} - \theta \right) = -\sin\left(\theta - \frac{\pi}{2}\right)= \cos\theta[/tex]
Therefore:
[tex]\displaystyle \sin\left(\theta - \frac{\pi}{2}\right) = -\cos\theta = -(-0.14) = 0.14[/tex]
Hence, our answer is D.
