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Rotate the yellow dot to a location of 2pi radians. After you rotate the angle, determine the value of tan 2pi, to the nearest hundredth.

Rotate the yellow dot to a location of 2π 2 \pi radians. After you rotate the angle, determine the value of tan⁡2π \tan 2 \pi , to the nearest hundredth.

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Full solution

Q. Rotate the yellow dot to a location of 2π 2 \pi radians. After you rotate the angle, determine the value of tan⁡2π \tan 2 \pi , to the nearest hundredth.
  1. Understand unit circle: Understand the unit circle and the angle rotation.\newlineRotating a point on the unit circle by 2π2\pi radians brings the point back to its starting position at (1,0)(1,0), which corresponds to an angle of 00 radians since 2π2\pi radians is equivalent to one full rotation around the circle.
  2. Recall tangent function: Recall the definition of the tangent function. The tangent of an angle in the unit circle is the ratio of the y-coordinate to the x-coordinate of the point on the unit circle at that angle. For the angle 2π2\pi, the point on the unit circle is (1,0)(1,0).
  3. Calculate tan⁡(2π)\tan(2\pi): Calculate the value of tan⁡(2π)\tan(2\pi).\newlineSince the point at angle 2π2\pi is (1,0)(1,0), the y-coordinate is 00 and the x-coordinate is 11. Therefore, tan⁡(2π)=yx=01=0\tan(2\pi) = \frac{y}{x} = \frac{0}{1} = 0.
  4. Round to nearest hundredth: Round the value of tan⁡(2π)\tan(2\pi) to the nearest hundredth.\newlineSince tan⁡(2π)\tan(2\pi) is 00, rounding to the nearest hundredth is not necessary, and the value remains 00.

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