Question

Find an exact value of cos 165 degrees help :)?

Answer 1

For the answer to the question above asking to find the exact value of cos 165 degrees.

The answer to this question is 
cos 165 = cos (120+45) 
= cos120 cos 45 - sin 120 sin 45 
= (-1/2)(sqrt(2)/2) - (sqrt(3)/2)(sqrt(2)/2) 
= (-sqrt(2) - sqrt(6))/4 
I hope my answer helped you. Have a nice day!

Answer 2

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 45*cos 30+sen45*sen30

$cos 15=\frac{\sqrt{2}}{2}*\frac{\sqrt{3}}{2} +\frac{\sqrt{2}}{2}*\frac{1}{2}= \frac{\sqrt{6+2}}{4}$

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