QQuestionMathematics
QuestionMathematics
Find the exact value of cos(2π/ 3) in its simplest form with a rational denominator.
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Answer
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Step 1:I'll solve this step-by-step using the precise LaTeX formatting guidelines:
Step 2:: Recall the cosine of special angle formula
The angle $$2\pi/3$$ is a standard angle in trigonometry.
We can solve this by understanding its position on the unit circle.
Step 3:: Analyze the angle's location
2\pi/3$$ is equivalent to $$120$$ degrees.
This is in the second quadrant of the unit circle.
Step 4:: Use the cosine double angle formula
We know that $$\cos(2\pi/3) = \cos(120^{\circ})
Step 5:: Recall the cosine value for 120 degrees
\cos(120^{\circ}) = -\frac{1}{2}
Step 6:: Verify the result
This can be confirmed by the unit circle coordinates or by trigonometric identities.
Final Answer
The solution is exact, in its simplest form, and has a rational denominator as requested.
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