21. if $\\cos 25^{\\circ}=.9063$, find $\\cos 155^{\\circ}$.
21. if $\\cos 25^{\\circ}=.9063$, find $\\cos 155^{\\circ}$.
Answer
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)