9514 1404 393
Answer:
[tex]\text{(a)} \quad -\dfrac{\sqrt{2+ \sqrt{3}}}{2}[/tex]
Step-by-step explanation:
The angle is near π, so the cosine value is a negative value near -1. This means the value under the numerator radical must be slightly less than 4. The only answer choice that makes any sense is the first choice.
The value of the cosine is ...
cos(11π/12) ≈ -0.9659
The values of the answer choices are ...
a) -0.9659 . . . . matches the required value
b) -0.2588
c) 0.2588
d) 0.9659
_____
You could use half-angle or angle sum formulas to figure this exactly, but it is much easier to make a multiple-choice selection based on your general knowledge of the cosine function and √3 (≈1.73).
