Question

1. if $\cos 25^{\circ}=.9063$, find $\cos 155^{\circ}$.

Explanation:

Step1: Use the cosine of supplementary angles formula

We know that \(\cos(180^{\circ}-\alpha)=-\cos\alpha\). Here, \(\alpha = 25^{\circ}\) and \(155^{\circ}=180^{\circ}-25^{\circ}\).
So, \(\cos155^{\circ}=\cos(180^{\circ} - 25^{\circ})\)

Step2: Substitute the value of \(\cos25^{\circ}\)

Since \(\cos(180^{\circ}-\alpha)=-\cos\alpha\), when \(\alpha = 25^{\circ}\), we have \(\cos(180^{\circ}-25^{\circ})=-\cos25^{\circ}\)
Given that \(\cos25^{\circ}=0.9063\), then \(\cos155^{\circ}=- 0.9063\)

Answer:

\(-0.9063\)