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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 $2 \pi$ radians. After you rotate the angle, determine the value of $\tan 2 \pi$ , to the nearest hundredth.

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Inverses of trigonometric functions using a calculator

Full solution

Q. Rotate the yellow dot to a location of

2 \pi

radians. After you rotate the angle, determine the value of

\tan 2 \pi

, to the nearest hundredth.

Understand unit circle: Understand the unit circle and the angle rotation. $\newline$ Rotating a point on the unit circle by $2\pi$ radians brings the point back to its starting position at $(1,0)$ , which corresponds to an angle of $0$ radians since $2\pi$ radians is equivalent to one full rotation around the circle.
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 $2\pi$ , the point on the unit circle is $(1,0)$ .
Calculate $\tan(2\pi)$ : Calculate the value of $\tan(2\pi)$ . $\newline$ Since the point at angle $2\pi$ is $(1,0)$ , the y-coordinate is $0$ and the x-coordinate is $1$ . Therefore, $\tan(2\pi) = \frac{y}{x} = \frac{0}{1} = 0$ .
Round to nearest hundredth: Round the value of $\tan(2\pi)$ to the nearest hundredth. $\newline$ Since $\tan(2\pi)$ is $0$ , rounding to the nearest hundredth is not necessary, and the value remains $0$ .

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