Find tan left(frac{2 pi}{3}right). Enter " U " if it is undefined.

Question

Accepted Answer

Step:1 ：The problem is to find the value of (tan left(frac{2 pi}{3}right)).Step:2 ：The tangent function is defined as the ratio of the sine to the cosine of an angle.Step:3 ：In the unit circle, the angle (frac{2 pi}{3}) is in the second quadrant where sine is positive and cosine is negative.Step:4 ：Therefore, the tangent of this angle will be negative.Step:5 ：The exact value of (tan left(frac{2 pi}{3}right)) is approximately -1.732, which is the square root of 3.Step:6 ：So, the tangent of (frac{2 pi}{3}) is (-sqrt{3}).Step:7 ：Final Answer: (boxed{-sqrt{3}})

Answer

Step: 1 ：The problem is to find the value of (tan left(frac{2 pi}{3}right)).Step: 2 ：The tangent function is defined as the ratio of the sine to the cosine of an angle.Step: 3 ：In the unit circle, the angle (frac{2 pi}{3}) is in the second quadrant where sine is positive and cosine is negative.Step: 4 ：Therefore, the tangent of this angle will be negative.Step: 5 ：The exact value of (tan left(frac{2 pi}{3}right)) is approximately -1.732, which is the square root of 3.Step: 6 ：So, the tangent of (frac{2 pi}{3}) is (-sqrt{3}).Step: 7 ：Final Answer: (boxed{-sqrt{3}})

Find $\tan \left(\frac{2 \pi}{3}\right)$. Enter " $U$ " if it is undefined.

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