Answer:
-0.965
Step-by-step explanation:
The cos 165 is on the Quadrant II. The symmetrical arc of 165º is 15º on the Quadrant I.
So we can say that cos 15º = -cos 165º since on the second quadrant the values for the cosine are negative.
cos (45º-30)= cos 45cos 30+sen45sen30
\(cos 15=\frac{\sqrt{2}}{2}*\frac{\sqrt{3}}{2} +\frac{\sqrt{2}}{2}*\frac{1}{2}= \frac{\sqrt{6+2}}{4}\)
cos 165 =-\(-\frac{\sqrt{6+2}}{4}\)
But on this form, there is an irrational number like √2 so the exact value would something approximately
cos 165 =-\(-\frac{\sqrt{6+2}}{4}\)≈-0.965
